the conjuction of a conditional statement and its converse

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a statement formed by joining 2 or more statements

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a statement that can be written in if-then form

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the statement formed by negating both the hypothesis and the conclusion of a conditional statement

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the statement formed by exchanging the hypothesis

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a false example

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a system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions

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in a conditional statement, the statement that immediatley follows the word if

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the statement formed by negating both the hypothesis and the conclusion of a conditional statement

ex: ~q^~p

negation

if a statement is represented by p then not p is the negation of the statement

ex: ~p

a rule that can justify your reasoning

ex: symmetric: a=b b=a

a statement or conjecture that can be proven true by undefined terms, definitions, and postulate

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two angles on the exterior that are congruent and on opposite sides

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2 angles that are on opposite sides of the interior and are congruent

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angles that are beside each other in the interior and equal 180

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angles that are the same measure

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coplanar lines that do not intersect

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lines that do not intersect and are not coplanar

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a line that intersects 2 or more lines in a plane at a different point

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a traiangle in which all of the angles are acute angles

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in a triangle, a segment from a vertex of the triangle to the line containing opposite side and perpendicular to the side

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the point of concurrency of the medians of a triangle

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the point of concurrency of the perpendicular bisectors of a triangle

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an equal measure to something else

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a graph used to find the missing coordinates

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a statement that can be easily proved using a theorem

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an angle formed by one side of a triangle and the extension of another side

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the side opposite the right triangle

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a triangle with at least 2 sides congruent

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two congruent sides of a right triangle

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in a triangle a line segment with endpoints of a vertex of a triangle and the midpoint of a side opposite the vertex

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a triangle with one angle of measure greater than 90

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a line, segment, or a ray that passes through the midpoint of a side and is perpendicular to that side

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the point of intersection of concurrent lines

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the angles of a triangle that are not adjacent to a given exterior angle

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a triangle with no 2 sides congruent

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2 nonadjacent angles formed by 2 intersecting lines

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reasoning that assumes that the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis or accepted fact

ex: x=10

x doesn't = 10

in an indirect proof, one assumes that the statement is to be proven false

ex: if B is the midpoint of line LH and LH is 36 then line BH is not congruent to line LB

if any lines contain any point in the interior

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if no points are in the interior

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a segment whose endpoints are the midpoints of 2 sides of the triangle

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a closed figure whose sides are all segments

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an equation of the form a/b = c/d that states the 2 ratios are equal

ex: 2/3 = 6/9

a convex polygon in which all sides are congruent and all angles are congruent

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the ratio of 2 lengths of 2 corresponding sides of 2 similar polygons or solids

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corresponding angles are congruen and measures of the corresponding sides are proportional

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A segment that is drawn from the center of a regular polygon perpendicular to a side of a polygon

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using the principles of length and area to find the probabilty of an event

example:  part/whole

a figure that cannot be classified as a single polygon

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a region of a circle bounded by a central angle and its intercepted arc

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the region of a circle bounded by an arc and a chord

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the angles that are directly above or below each other

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a shape with 10 sides

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In a polygon, a segment that connects nonconsecutive vertices of a polygon

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A shape with 12 sides

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the sum of the exterior angles always equals 360

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a shape with 6 sides

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a shape with 7 sides

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the sum of the interior angles equals 180(n-2)

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a trapezoid in which the legs are congruent

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a quadrilateral with exactly 2 distinct pairs of adjacent congruent sides

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the segment that joins the midpoints of the legs

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a polygon with n-sides

ex: 180(n-2)

a polygon with 8 sides

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the angles that are diagonal from each other

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the sides that are across from each other in a quadrilateral

Line a and line c are examples

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a quadrilateral with parallel opposite sides

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a shape with 5 sides

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the side lengths of all sides added together

ex: the perimeter of this shape is 19

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a shape with 4 sides

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a quadrilateral with 2 opposite sides parallel and congruent and another 2 sides parallel and congruent with all angles being right angles

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a quadrilateral with all 4 sides congruent

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a quadrilateral with all four sides and angles congruent

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a quadrilateral with 1 pair of parallel lines

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the parallel sides of a trapezoid

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the height of a trapezoid from the bases which forms a right angle

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a part of a circle that is defined by two endpoints

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the given point that is in the middle of the circle

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an angle whose vertex is te center of a circle

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a segment with both endpoints on the circle

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the set (focus) of all points in a plane equidistant from a given point

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the distance around a circle

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a circle is circumscribed about a polygon if the circle contains all the vertices of the polygon

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a chord that passes though the center

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a polygon is inscribed in a circle if each of its vertices lie in the circle

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an angle intercepts an arc if the endpoint of the arc lie on the angle, all points of the arc (except endpoints) are in the interior of the circle, and each side of the angle contains an endpoint of the arc

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360 - measure of minor arc>180

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the central angle<180

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the irrational number represented by the ratio of the circumference of a circle to the diameter of a circle

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a segment with 1 endpoint on the center

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any line that intersects a circle in exactly two endpoints

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half a circle and measure equals 180 degrees

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a line in the plane of a circle that intersects the circle in exactly 1 point

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the angle betweent the line of sight and the horizontal line when an observer looks downward

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the angle between the line of sight and the horizontal line when an observer looks upward

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a segment from a vertex of the triangle to the line containing the opposite side and perpendicular to that side

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for an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the hypotenuse

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for any positive numbers a and b, the positive number x such that a/x=x/b

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the identity cos² θ + sin² θ=1

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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

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finding the measures of all the angles and sides of a triangle

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For an acute angle of a right triangle, the ratio of the measures of the leg opposite the acute angle to the measure of leg adjacent

ex: opposite/tangent

to the acute angle, the study of the properties of triangles and trignometric functions and their applications

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an angle with a measure that is less the 90 degrees

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an amount between two points.

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lines that form right angles

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a flat surface made up of points that has no depth and extends infinitely

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2 angles that lie in the same plane, have a common vertex, and a common side, but no common interior points

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the inside angles in a polygon

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a location in a plane

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the intersection of two noncollinear rays at a common endpoint

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made up of points  and has no thickness or width

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a statement that describes a fundamental relationship between the basic terms of geometry

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a ray that divides an angle into 2 congruent parts

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a measurable part of a line that consists of 2 endpoints, and all of the points in between them

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a line that goes in one direction infinitely

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points that lie on the same plane

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a pair of adjacent angles whose noncommon sides are opposite rays

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an angle with the measure of 90 degrees

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adjacent angles whose measure, when added together, equal 90 degrees

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the exact middle in a line segment

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a sgment, line, or a plane that intersects a segment at its midpoint

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having the same measure

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an angle with a measure more than 90 degrees but less than 180 degrees

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a boundless 3-D set of all points

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two rays that share a common endpoint and go infinitely in opposite directions

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two angles with measures that have a sum of 180

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a unit of measure used in measuring angles and arcs

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point, line, and plane are the undefiend terms in geometry

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the common endpoint

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two nonadjacent angles formed by 2 intersecting lines

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a proof that uses arrows to show the conclusions made from the given to get to the the end result

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written in the form if p, then q, which p is the hypothesis and q is the conclusion

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Paragraph Proof

A proof that is written by using complete sentences that makes conclusion from the given statements to get to the end conclusion

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reasoning that uses a number of specific examples to arrive at generalization or prediction

ex: All the ice that has been examined has been cold. Therefore, all ice is cold.

a logical argument in which each staement you make is supporte by a statement that is aceepted as true

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a proof that has two columns; one that as the steps and the other has the reasons

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the distance between two lines measured along a perpendicular line to the lines is always the same

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corresponding parts of a congruent triangle are congruent

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side-angle-side which is used as a way to prove that two triangles are congruent

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side-side-side is used as a way to prove that 2 triangles are congruent

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angle-side-angle is used as a way to prove that two triangles are congruent

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angle-angle-side is a way to prove that 2 triangles are congruent

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two triangles that overlap each other and are congruent

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in a/b=c/d, the numbers a and d

ex:

sinA/a=sinB/b=sinC/c in triangle ABC

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in a/b= c/d, the numbers b and c

ex: 4/5=12/15 if and only if 4 x 15=5 x 12 therefore 4and 12 would be the means 

a comparison of 2 quantities

ex: 1:2

In triangle ABC, a²=b²+c²-2bc(cosA)

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a circle with a radius of one, centered at the origin, and is commonly used in trignometry

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a polygon with 11 sides

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do not intersect the segment connecting the centers

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intersect the segment connecting the centers

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circles that have the same center but different radi

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  tangent circles such that one circles lies outside the other.

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 two tangent circles such that one circle lies inside the other.

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this is required along with a scale factor in order to do a dilation

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the fixed point of a rotation

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a matrix containing one column often used to represet an ordered pair

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the x value in a matrix

ex:the n is the columns

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successive reflections in parallel lines

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a transformation that is determined by a center point and a scale factor that enlarges or shrinks a figure

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a matrix that when multiplied with another leaves the matrix the same

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the shape of a polygon

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a mappig for which the original figure and its image are congruent

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graphing the pre-image and the the image on a coordinate plane

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what the shape looks like before it goes through a transformation

ex: the blue is the preimage

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reflection

a transformation representing a flip of the figure over a point

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a matrix that cna 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 the center of rotation

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a matrix that can be multiplied by the vertex matrix of a figure to find the coordiantes of the rotated image

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one row is the x and the other row is the y

ex: m is the rows

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a constant multiplied by a vector

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the matrix that is the operator

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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 t0 the vertx matrix of a figure to find the coordinates of a translated image

ex: <x+a, y+b>

the matrix for the vertices in an image

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the distance between 2 bases

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2 parallel congruent faces

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a solid with a circular base, a vertex, and a lateral surface area

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2 solids are congruent if the corresponding angles are congruent, edges are congruent, corresponding faces are cngruent, and the volumes are congruent.

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a hexahedron-has 6 sides and all faces are square

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a figure with bases that are formed by congruent circles in parallel planes

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line segments where the faces intersect

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each flat surface

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a given sphere, the intersection of the sphere and a plane that contains the center of the sphere

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how high a 3d figure is

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one of the 2 congruent pairs into which a great circle seperates a sphere

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the area of the figure excluding the bases

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in a prism, the faces that are not bases

in a pyramid, the edges of the lateral faces that join the vertex to vertices of the bases

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a 2D figure that when folded forms a 3d figure

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a figure in which the lateral edges are not perpendicular to the base

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5 regular polyhedron: tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron

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has 12 faces and the shape of all the faces is a pentagon

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has 6 faces and the shape of all the faces is a square

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has 20 faces and all of the faces are equilateral triangles

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has 8 faces and all faces are equilateral triangle

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has 4 faces and all are faces are the shape of an equilateral triangle

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closed 3d figures made up of flat polygonal regions

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a solid that ahs 2 bases formed by congruent polygons that lie in parallel planes, has lateral faces, and lateral edges are parallel

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a solid that all of its faces except on intersects at the vertex , has a base , and lateral faces are triangular

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a figure in which its lateral edges are altitudes

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a polyhedron in which all of the faces are regular congruent polyhedron

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shapes that have the exact same shape but not the same size

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the height of each lateral face

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a round shape that doesn't have any edges or faces

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the sum of the areas of each face of the solid

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a point that connects 2 line segments

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a measure of amoun of space enclosed by a 3d figure

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