Term
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Definition
An angle less than 90 degrees but more than 0 degrees
An angle measuring 35 degrees |
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Term
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Definition
The property created by the space between two objects or points
The distance from point A to point B is 15 cm |
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Term
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Definition
Two lines that intersect to form right angles
The x axis and the y axis on a graph are perpendicular lines |
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Term
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Definition
A triangle in which all three angles are acute
A triange with all angles measuring 60 degrees |
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Term
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Definition
Every point not included in any given figure
Every point outside of a hexagon |
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Term
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Definition
An undefined term, has no space but is a flat mass of points that extends forever in all directions
The x and y axis form a plane |
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Term
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Definition
Angles that have a common ray coming out of the vertex going between two other rays
Supplementary angles are usually also adjacent angles |
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Term
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Definition
Every point included in any given figure
All the points contained in a hexagon |
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Term
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Definition
An undefined term, any given spot on a plane, has no extension
Point (3,0) on a graph |
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Term
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Definition
A figure formed by two lines, line segments, or rays that are connected at a point
The intersection of line AB and line CB creates an angle |
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Term
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Definition
A row of points that extends infinitely in both directions
The x-axis is a line |
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Term
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Definition
A proposition that is not proved or demonstrated but is accepted as true
"A line is defined by any two points" is a postulate |
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Term
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Definition
A line, line segment, or ray that cuts an angle in half exactly
Line BD bisects angle ABC |
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Definition
A portion of a line that has a begenning point and an endpoint
Line segment AB inside of line AC |
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Term
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Definition
A line that has an endpoint and extends forever in one direction
Ray AB -------> |
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Term
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Definition
Two points are collinear if they are on the same line
Points A and B are collinear on line CD |
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Term
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Definition
The two supplementary adjacent angles formed by two intersecting lines
What is formed when the y-axis intersects the x-axis |
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Term
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Definition
An angle which measures 90 degrees exactly
Perpendicular lines form right angles. Squares are made up of right angles |
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Term
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Definition
Two angles that add up to 90 degrees
An angle measuring 40 degrees and an angle measuring 50 degrees would be complimentary |
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Term
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Definition
A point exactly in the middle of a line segment
The midpoint of a line segment with endpoints at (1,0) and (3,0) would have a midpoint at (2,0) |
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Term
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Definition
Any line, segment or ray that intersects a segment at its midpoint
Line AB intersects line CBD at point B, the midpoint |
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Term
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Definition
Having the same shape, size, and angles
A square with area of 20cm is congruent to a square with an area of 20cm |
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Term
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Definition
An angle with a measure of over 90 degrees
An angle with a measure of 100 degrees |
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Term
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Definition
The state of being on the same plane as another figure
Line A and line B both being on plane C |
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Term
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Definition
Collinear rays with the same endpoint.
Two rays with the same endpoint that look like one line |
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Term
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Definition
The set of all possible points; made up of infinite planes
Point B, (5,0) |
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Term
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Definition
A pair of angles whose measures add up to 180 degrees
Angle A measures 70 degrees and angle B measures 110 degrees |
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Term
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Definition
The unit angles are measured in
A triangle always has 180 degrees |
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Term
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Definition
A line, or line segment, that intersects a given line segment at its midpoint and forms right angles
Line A intersects line B creating two 90 degree angles and cutting line A at its midsegment |
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Term
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Definition
The undefined terms in geometry are line, point, plane, and set
Line A, point B, plane C, and the set of point D |
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Term
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Definition
The point of intersection of lines or the point opposite the base of a figure
Lines A and B intersect at point C, the vertex |
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Term
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Definition
The pair of angles that are directly across from each other when two straight lines intersect
Angle A and angle B are verticle angles |
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Term
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Definition
A logical operator connecting two statements to assert "p if and only if q", where p is a hypothesis and q is a conclusion
It is raining if and only if there are clouds in the sky |
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Term
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Definition
A compound statement formed by joining two or more statements with the word and
It is raining and there are clouds in the sky |
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Term
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Definition
The proposition arrived at by logical reasoning
If it is raining, then THERE ARE CLOUDS |
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Term
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Definition
An "if then" statement. If P, then Q
If it is raining, there are clouds |
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Term
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Definition
A conjecture is a proposition that is unproven but appears correct and has not been disproven
Sum of the measures of the interior angles in any triangle is 180 degrees |
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Term
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Definition
A statement where hypothesis and conclusion are reversed and negated, if not P then not Q
"If the sum of the figures angles does not equal 180, then it is not a triangle." As opposed to "If it is a triangle then the sum of its angles is 180 degrees." |
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Term
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Definition
A statement where the hypothesis and conclusion are reversed, if Q then P
"If the sum of the figure's angles is 180, then it is a triangle." As opposed to "If the figure is a triangle, then the sum of its angles is 180 degrees." |
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Term
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Definition
A specific example used to disprove something
Statement: "When you multiply two numbers the answer is always even." Counterexample: "3x1=3" |
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Term
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Definition
The process of reasoning logically from given statements to a conclusion
If triangle ABC has angles A 90 degrees, B 45 degrees, and C 45 degrees, than you can reason that it is a right triangle, because right triangles contain one 90 degree angle |
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Term
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Definition
A proof containing boxes and arrows containing statements and reasons that is used to prove a statement true |
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Term
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Definition
An educated guess, the IF part of an if...then statement
"If a plant does not get water," |
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Term
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Definition
A statement made in the form of "If this, then that"
"If a plant does not get water, then it will die." |
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Term
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Definition
A process in which you make a conclusion based on known fact and observation, or repetition and pattern
If today is Saturday, then i know tomorrow will be Sunday because Sunday always comes after Saturday, and that is how the week is named |
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Term
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Definition
A statement in which both P and Q are negative, If not P then not Q
If it is not Saturday then tomorrow will not be Sunday As opposed to If today is Saturday then tomorrow will be Sunday |
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Term
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Definition
An operation on propositions, makes something the opposite of what it was.
The sentance "It is sunny" is negated by adding not, "It is not sunny" |
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Term
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Definition
A two-column proof written in paragraph form.
A two-column proof not written within a column but instead in a block paragraph |
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Term
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Definition
A system that uses logic to prove a statement using properties and given statements
Prove: Circle A is equal to Circle B Given: The radius of Circle A is 5, and the radius of Circle B is 5 |
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Term
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Definition
An attribute of an object, a fact about something that is specific to that object.
Addition and multiplication have the commutative property |
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Term
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Definition
A declaritive statement that is either true or false
It is raining |
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Term
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Definition
A statement that is proved true on the basis of previously established statements
A triangle has 180 degrees |
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Term
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Definition
A proof where the statements are in one column and the reasons are in another, used to prove statements true or false |
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Term
Alternate Exterior Angles |
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Definition
Angles located outside a set of parallel lines and on opposite sides of the transversal |
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Term
Alternate Interior Angles |
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Definition
Angles located inside a set of parallel lines and on opposite sides of the transversal |
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Term
Consecutive Interior Angles |
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Definition
Angles on the same side of the transversal
They can also be lateral angles |
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Term
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Definition
Two angles in the same relative position on two lines when those lines are cut by a transversal
If you were to slide the lines ontop of eachother, they would be in the same place |
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Term
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Definition
All points being equally distant from another point
The points on the edge of a circle |
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Term
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Definition
Lines that will never intersect
The yellow lines on a highway are parallel |
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Term
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Definition
Planes that will never intersect
Pages in a book are parallel planes |
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Term
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Definition
Lines that should intersect, but do not because they lay in different
Lines that arent parallel drawn on two peices of paper that are flat on top of eachother would be skew lines |
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Term
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Definition
A line that cuts between two parallel lines
The back line of the letter F is a transversal |
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Term
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Definition
The angle formed where two lines meet
The intersection of line A and line B create an included angle, C |
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Term
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Definition
The side between two consecutive angles of a polygon
In a hexagon, if the lines are numbered 1-6 clockwize and the angles A-F clockwize, line 2 between angles A and B would be the included side |
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Term
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Definition
The side of a right triangle opposite the right angle
The slanted side of a right triangle |
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Term
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Definition
The verticle and horozontal lines in a triangle
A and B in the Pythagorean theorem |
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Term
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Definition
Congruent parts of a triangle are congruent
If triangle ABC is congruent to DEF, then angle A and angle D are congruent |
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Term
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Definition
Side Angle Side
On triangel ABC and DEF, sides A and D, and B and E are congruent, and angles a and b are congruent |
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Term
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Definition
Side Side Side
In triangle ABC and DEF, all matching sides are congruent |
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Term
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Definition
Angle Side Angle
In triangle ABC and DEF, angle a and d are congruent, side B and E are congruent, and angle b and e are congruent |
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Term
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Definition
Angle Angle Side
In triangle ABC and DEF, angles a and d are congruent, angles b and e are congruent, and sides B and E are congruent |
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Term
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Definition
Reasoning using the Law of the Contrapositive, the Law of Ruling Out Possibilities, or the Law of Indirect Reasoning
On a multiple choice question, i know the answer is not A, B, or C because those are all imposible |
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Term
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Definition
A proof where the prove is taken as false and continues to prove it is false, untill the proof arives at a contradiction and the prove is proved true
Prove: 2 does not equal 2
The contradiction would be that a number always equals itself, therefore, one cannot assume that 2 does not equal 2 |
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Term
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Definition
Two triangles that overlap
Triangle ABC and triangle DEC overlapping at point C |
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Term
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Definition
In a proportion, the top number of the first fraction and the bottom number of the second fraction
In a/b = c/d, a and d |
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Term
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Definition
In a proportion, the bottom number of the first fraction and the top number of the second fraction
In a/b = c/d, b and c |
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Term
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Definition
An equation stating that two ratios are equal
A/B = C/D |
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Term
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Definition
A comparison of two quantities
A:B |
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Term
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Definition
The ratio used when comparing measurements of corresponding things, such as sides or angles
The ratio of the real house to the model house is 10:1 |
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Term
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Definition
Having the same shape
Two equilateral triangles are always similar, regarless of the size |
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Term
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Definition
A shape with many sides
A square is a polygon |
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Term
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Definition
A shape for which there is a line containing a side of the polygon that also contains a point in the interior of the polygon
If you were to extend all the lines in a concave polygon, some would go through the interior of the shape |
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Term
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Definition
A shape for which there is no line that contains both a side of the polygon and a point in the interior of the polygon
If you can extend all the lines that make up the polygon and none go through the middle, it is a convex polygon |
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Term
Mid-segment of a Triangle |
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Definition
A segment with endpoints that are thee midpoints of two sides of a triangle
The sides of equilateral triangle ABC all measure 6 inches. The median would be 3 inches up from the begenning of the side and stretch to the other side of the triangle |
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Term
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Definition
When all the sides in a figure are congruent and all of the angles are congruent
The Pentagon is a regular pentagon |
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Term
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Definition
Two polygons whos angles are congruent and whos sides are proportonate
Equilateral triangles are similar |
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Term
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Definition
The angle between the line of sight and the horizontal when an observer looks downward
The top angle in the letter Z is the angle of depression |
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Term
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Definition
The angle between the line of sight and the horizontal when an observer looks upward
The bottom angle in the letter Z is the angle of elevation |
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Term
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Definition
For an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse
Cos62=3/5 |
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Term
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Definition
For any positive numbers A and B, the positive number X such that A/X=X/B
9/X=X/12 |
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Term
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Definition
A group of three whole numbers that satisfies the equation A^2+B^2=C^2, where C is the greatest number
3, 4, and 5 are a Pythagorean triple |
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Term
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Definition
For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse
Sin42=12/14 |
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Term
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Definition
Finding the measures of all of the angles and sides of a triangle
A= a= B= b= C= c= |
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Term
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Definition
For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle
Tan12=2/13 |
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Term
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Definition
The study of the properties of triangles and trigonometric functions and their applications |
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Term
Altitude Of A Right Triangle |
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Definition
A segment from a vertex of the triangle to the line containing the opposite side and perpendicular to that side
In triangle ABC, the line that begins at point A and is perpendicular to line BC is the altitude |
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Term
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Definition
Let ABC be any triangle with a, b, and c representing the measures of sides opposite the angles with measures A, B, and C respectivley. Then, sinA/a=sinB/b=sinC/c
sin90/5=sin60/4=sin30/3 |
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Term
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Definition
Let ABC be any triangle with a, b, and c representing the measures of sidese oppositee the angles with measures A, B, and C respectivley. Then the following equations are true; a^2 = b^2 + c^2 - 2bc cosA b^2 = a^2 + c^2 - 2ac cosB c^2 = a^2 + b^2 - 2ab cosC
5^2=3^2+4^2-2(3)(4)cos90 |
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Term
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Definition
The circle with a radius of one and the center point at the origin, (0,0). |
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Term
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Definition
In a polygon, a segment that connects nonconsecutive vertices of the polygon
In polygon PQRS, line QS is a diagonal |
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Term
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Definition
A trapezoid in which the legs are congruent, both pairs of base angles are congruent, and the diagonals are congruent
If you draw a square, flat surface using depth, it should look like an isoceles trapezoid |
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Term
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Definition
A quadrilateral with exactly two distinct pairs of adjacent congruent sides
A traditional diamond shape is a kite |
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Term
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Definition
The segment that joins the midpoints of the legs
In trapezoid ABCD, the median runs from the middle of leg BC to the middle of leg DA |
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Term
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Definition
A quadrilateral with parallel opposite sides. Any side of a parallelogram can be called a base.
In quadrilateral ABCD, lines AB and CD are parallel, and lines AD and BC are parallel |
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Term
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Definition
A quardrillateral with four right angles
A book is often a rectangle |
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Term
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Definition
A quadrilateral with all four sides congruent
A square is a rhombus, but a rhombus may also be more diamond-shaped |
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Term
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Definition
A quadrilateral with four sides and four angles congruent
The bases in baseball are squares |
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Term
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Definition
A quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases. The nonparallel sides are called legs. The pairs of angles with their vertices at the endpoints of the same base are called base angles.
Foreheads are shaped like a trapezoid |
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Term
Consecutive Angles Of A Quadrilateral |
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Definition
The angles that are following eachother if you look at them clockwize or counterclockwize
In quadrilateral ABCD, A and B are consecutive angles |
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Term
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Definition
A ten-sided figure
Some coins are decagons |
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Term
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Definition
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Term
Exterior Angles Of A Polygon |
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Definition
An angle formed by one side of a polygon and the extension of another side
They always add up t 360 |
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Term
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Definition
A six-sided figure
The cells in a beehive are hexagons |
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Term
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Definition
A seven-sided figure
In photography, the flares are in the shapes of heptagons |
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Term
Interior Angles Of A Polygon |
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Definition
The inside angles on a polygon
Any angle that is created by two sides on any polygon |
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Term
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Definition
A polygon with any number of sides
A thirteen-sided figure is an N-Gon |
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Term
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Definition
A nine-sided figure
Tiles can be nonagons |
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Term
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Definition
An eight-sided figure
A stop sign is an octagon |
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Term
Opposite Angles Of A Quadrilateral |
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Definition
Angles that are opposite eachother
In square ABCD, angles B and D are opposite angles |
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Term
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Definition
A five-sided figure
The Pentagon is a pentagon |
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Term
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Definition
The sum of all the lengths of the sides of any figure
The length of a fence is the perimeter, a fence is a perimeter |
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Term
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Definition
A four-sided figure
A square is a quadrilateral |
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Term
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Definition
The parallel sides of a trapezoid
In trapezoid ABCD, lines AB and CD are the bases |
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Term
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Definition
The measure of a line drawn perpendicular to both bases of a trapezoid
The height of trapezoid ABCD is 13 |
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Term
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Definition
An eleven-sided figure
Any eleven-sided figure |
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Term
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Definition
A part of a circle that is defined by two endpoints
1/4 of the perimeter of a circle is an arc |
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Term
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Definition
The middle
The center of a graph is the origin (0,0) |
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Term
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Definition
An angle that intersects a circle in two points and has its vertex at the center of the circle
The cuts of a piece of pie are central angles |
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Term
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Definition
For a given circle or sphere, a segment with endpoints on the circle or sphere
If you begin at one point on the outside of the circle and draw a line to another place on the circle, that is a chord |
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Term
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Definition
The locus of all points in a plane equidistant from a given point called the center of the circle
When drawing a human, you first draw the joints as circles |
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Term
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Definition
The distance around a circle
Like the perimeter of a circle |
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Term
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Definition
A circle is circumscribed about a polygon if the circle contains al the vertices of the polygon
A square with all its angles touching the circle inside the circle |
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Term
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Definition
The tangent of two circles
On a conveyer belt, the belt around the wheels is the common external tangent |
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Term
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Definition
A tangent that is common to two circles and intersects the segment joining the centers of the circles is called Common Internal Tangent
If you draw an imaginary line between the stomach part and the head of a snowman, that is the common internal tangent |
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Term
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Definition
Concentric objects share the same center, axis or origin with one inside the other
A bullseye is made of concentric circles |
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Term
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Definition
The line that goes through the center of the circle with endpoints on the circle
If you fold a circle in half, the fold line is the diameter |
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Term
Externally Tangent Circles |
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Definition
Circles that touch but do not overlap
If you draw a flower out of circles, they should be externally tangent circles |
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Term
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Definition
An angle in a circle with its vertex on the edge of a circle
An inscribed polygon's angles are inscribed angles |
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Term
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Definition
Same as an inscribed polygon, a figure drawn inside a circle with endpoints on the circle
A square inside a circle would be an inscribed figure |
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Term
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Definition
An angle intercepts an arc if and only if each of the following conditions are met; 1. The endpoints of the arc lie on the angle 2. All points of the arc except the endpoints are in the interior of the circle 3. Each side of the angle contains an endpoint of the arc
Just about any angle drawn inside a circle where the ends of the angle are on the outside of the circle |
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Term
Internally Tangent Circles |
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Definition
Two circles, one of which is inside the other, that have a single point touching |
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Term
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Definition
An arc with a measure greater than 180 degrees
In a circle, an arc with a measure of 181 degrees |
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Term
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Definition
An arc with a measure of less than 180 degrees
In a circle, an arc with a measure of 179 |
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Term
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Definition
An irrational number represented by the ratio of the circumference of a circle to the diameter of the circle
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609... |
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Term
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Definition
For a line that intersects a circle in only one point, the point at which they intersect
Line AB tangent to line C, they intersect at point D, the point of tangency |
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Term
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Definition
Half of the diameter of a circle
If the diameter of circle A is 12, the radius is 6 |
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Term
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Definition
Any line that intersects a circle in exactly two points
If the diameter of a circle is extended, it is a secant |
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Term
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Definition
Half of a circle
If you take a circle and cut it in half, the halves are semicircles |
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Term
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Definition
A line in the plane of a circle that intersects the circle in exactly one point
If you draw a circle and then draw a line under the circle, the line is the tangent |
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Term
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Definition
A segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon
The apothem is similar to the radius of a circle |
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Term
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Definition
Using the principles of length and area to find the probability of an event
Finding how often a spinner will land on 1 out of 10 wedges |
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Term
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Definition
A figure that is not regular, all sides are not equal
A trapezoid is an irregular figure |
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Term
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Definition
A polygon that is not regular
A trapezoid is an irregular polygon |
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Term
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Definition
A region of a circle bounded by a central angle and its intercepted arc
If you cut a circle into fourths, one of the fourths would be a sector |
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Term
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Definition
The region of a circle bounded by an arc and a chord
If you draw a central angle inside a circle, then from each of the points where the angle meets the edge of the circle, you draw a straight line, the area between the edge of the circle and the straight line is the segment |
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Term
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Definition
A segment that is perpendicular to the bases or base and vertex
If you draw a straight line in the middle of a cone that ends at the point, that is the altitude |
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Term
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Definition
The two similar and parallel surfaces on a 3D figure
On a square, all the sides are bases |
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Term
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Definition
A solid with a circular base, a vertex not contained in the same plane as the base, and a lateral surface area composed of all points in the segments connecting the vertex to the edge of the base
An ice cream cone is a cone |
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Term
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Definition
Two solids are congruent if... 1. The corresponding angles are congruent 2. Corresponding edges are congruent 3. Corresponding faces are congruent 4. The volumes are congruent
Two identical dice from a board game are congruent solids |
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Term
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Definition
A 3D figure made of six squares
A dice is a cube |
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Term
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Definition
A figure with bases that are formed by congruent circles in parallel planes
A can is a cylinder |
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Term
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Definition
Where the faces of a solid meet
The corner of a desk is an edge |
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Term
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Definition
One of the 2D figures that makes up the 3D object
The base of a pyramid is a face |
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Term
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Definition
For a given sphere, the intersection of the sphere and a plane that contains the center of the sphere
The equator is a great circle |
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Term
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Definition
How tall a figure is
The height of the cone is 12 meters |
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Term
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Definition
One of the two congruent parts into which a great circle separates a sphere
The Northern Hemisphere is a hemisphere |
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Term
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Definition
For prisms, pyramids, cylinders, and cones, the area of the figure, not including the bases
The area of the label of a soup can would be the lateral area of the can |
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Term
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Definition
In a prism, the faces that are not bases In a pyramid, the faces that intersect at the vertex |
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A two dimensional figure that when folded form the surfaces of a three-dimensional object
_ |_|_ _ _ |_|_|_|_| |_| would be the net for a cube |
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Oblique.. Cone Cylinder Prism |
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A cone that is not a right cone A cylinder that is not a right cylinder A prism in which the lateral edges are not perpendicular to the bases
If you take a slinky and slide the top of it one way and the base another way while keeping all the rings touching, that is an oblique cylinder |
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The five regular polyhedra: tetrahedron, hexahedron, otcahedron, dodecahedron, or icosahedron |
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A solid figure with 12 regular pentagon faces
A twelve-sided Platonic solid |
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A polyhedron with six faces
A cube |
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A solid made of twenty equilateral triangles |
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A solid made of up eight triangular faces |
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A solid made up of four triangular faces |
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Closed 3D figures made up for flat polygonal regions. the flat regions formed by the polygons and their interiors are called faces. Pairs f faces intersect in segments called edges. Points where three or more edges intersect are called vertices
A cube |
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A solid with the following characteristics; 1. Two faces, called bases, are formed by congruent polygons that lie in parallel planes 2. The faces that are not bases, caled lateral faces, are formed by parallelograms 3. The intersections of two adjacent lateral faces are called lateral edges and are parallel segments
A Toblerone chocolate bar is a triangular prism |
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A solid with the following characteristics; 1. All of the faces, except one face, intersect at a point called the vertex 2. The face that does not contain the vertex is called the base and is a polygonal region 2. The faces meeting at the vertex are called lateral faces and are triangular regions
The Great Pyramid of Giza is a pyramid |
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A 3D figure with bases that are regular polygons |
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A cone with an axis that is also an altitude A cylinder with an axis that is also an altitude A prism with lateral edges that are also altitudes
Straight 3D figures |
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Solids that have exactly the same shape, but not necessarily the same size
Two cubes are similar solids |
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The slant height of a right circular cone is the distance from any point on the circle to the apex of the cone
In a pyramid, the hypotenuse of the right triangle formed by the apothem and the altitude |
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In space, the set of all points that are a given distance from a given point, called the center
The earth is a sphere |
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The sum of all the areas of all faces and side surfaces of a 3D figure |
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A measure of the amount of space enclosed by a 3D figure
How much water or air or anything a 3D figure holds |
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The top point of a pyramid, where all the faces except the base meet
The top of a pyramid is the vertices |
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What the figure is dilated about, usually the origin (0,0) |
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A fixed point around which shapes move in a circular motion to a new position
Point (3,3) could be a center of rotation |
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A matrix containing one column often used to represent an ordered pair or a vector
= [x] [y] |
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The vertical lines of data in a matrix |
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The application of one function to the results of another |
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A transformation determined by a center point C and a scale factor K. When K>0, the image P' of P is the point on line CP such that CP' = |K| x CP. When K<0, the image P' of P is the point on the ray opposite line CP such that CP' = k x CP
Making a figure larger or smaller |
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A scalar matrix in which all of the diagonal elements are unity
[ 1 0 ] [ 0 1 ] |
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A mapping for which the original figure and its image are congruent |
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a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function) |
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Original position of a figure in a plane |
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A transformation representing a flip of the figure over a point, line, or plane |
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A matrix that can be multiplied by the vertex matrix of a figure to find the coordinates of the reflected image |
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A transformation that turns every point of a preimage through a specified angle and direction about a fixed point, called the center of rotation |
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A matrix that can be multiplied by the vertex matrix of a figure to find the coordinates of the rotated image |
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The transpose of a row vector is a column vector |
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A constant multiplied by a vector |
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When the initial point of a vector is at the origin |
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A transformation that moves all points of a figure the same distance in the same direction |
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A matrix that can be added to the vertex matrix of a figure to find the coordinates of the translated image |
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A matrix that represents a polygon by placing all of the column matrices of the coordinates of the vertices into one matrix |
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