Term
|
Definition
The set of all points
Pg. 6 |
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Term
|
Definition
Points all in one line
Pg. 6 |
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|
Term
|
Definition
Points all in one plane
Pg. 6 |
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|
Term
|
Definition
Where two figures(lines, planes, or the combination
of both) meet or cut.
The set of points that are in both figures. Pg. 6 |
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Term
|
Definition
Shown by two letters(the endpoints) with a
line over it.
Constists of the endpoints and all points between
those endpoints. Pg. 11 |
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Term
|
Definition
Shown by two letters(one an endpoint named first and another) with an arrow going to the right over the top.
Consists of the endpoint and all points to and paste the second letter. Pg. 11 |
|
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Term
|
Definition
Rays that start at the same endpoint, but go
in opposite direction. Pg. 11 |
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Term
|
Definition
Shown by two letters(the endpoints).
Subtract the coordinates of it endpoints. Pg. 11 |
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Term
|
Definition
Statements that are accepted wihout proof
Pg. 12 |
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Term
|
Definition
1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinantes 0 and 1.
2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates. Pg. 12 |
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|
Term
Segment Addition
Postulate |
|
Definition
If B is between A and C, then
AB + BC = AC
PG. 12 |
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Term
Congruent and
Congruent Segments |
|
Definition
Two objects that have the same size and shape.
Two segements that have equal length.
Pg. 13 |
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Term
|
Definition
The point that divides the segment into two congruent segements.
Pg. 13 |
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Term
|
Definition
A line, segment, ray, or plane that intersects the segment at its midpoint.
Pg. 13 |
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Term
|
Definition
The figure formed by two rays that have the same endpoint.
Pg. 17 |
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|
Term
Sides &Vertex
of an angle |
|
Definition
Sides - the two rays that form the angle
Vertex - the common endpoint of the rays that form the angle
Pg. 17 |
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|
Term
|
Definition
Measure between o and 90
Pg. 17 |
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Term
|
Definition
|
|
Term
|
Definition
Measure between 90 and 180
Pg. 17 |
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|
Term
|
Definition
|
|
Term
|
Definition
On line AB in a given plane, choose any point 0 between A and B. Consider line OA and line OB and all the rays that can be drawn from o on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that:
a. Line OA is paired with 0, and line OB with 180.
b. If line OB is paired with x, and line OQ with y, then m ‹ POQ = ǀx-yǀ Pg. 18 |
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Term
|
Definition
If point B lines in the interior of <AOC, then
m< AOB + m< BOC = m< AOC
If < AOC is a straight angle and B is any point not on line AC, then
m< AOC + m< BOC = 180 Pg. 18 |
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|
Term
|
Definition
Angles that have equal measures
Pg. 19 |
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|
Term
|
Definition
Two angles in a plane that have a common vertex and a common side but no common interior points
Pg. 19 |
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Term
|
Definition
The ray that divides that angle inot two congruent adjacent angles.
Pg. 19 |
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|
Term
Postulate 5
# of points in a line |
|
Definition
A Line contains at least two points; a plane contains at least three points not all in one line; space contaoins at least four points not all in one plane.
Pg. 23 |
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|
Term
Postulate 6
Forming a line |
|
Definition
Through any two points there is exactly one line.
Pg. 23 |
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|
Term
Postulate 7
# of points in a plane |
|
Definition
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.
Pg. 23 |
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|
Term
Postulate 8
Lines in a plane |
|
Definition
If two points are in a plane, then the line that contains the points is in that plane.
Pg. 23 |
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|
Term
Postulate 9
Intersecting planes |
|
Definition
If two planes interest, then their intersection is a line.
Pg. 23 |
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|
Term
Theorem 1-1
Intersecting lines |
|
Definition
If two lines intersect, then they intersect in exactly one point.
Pg. 23 |
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|
Term
Theorem 1-2
Forming a plane |
|
Definition
Through a line and a point not in a line there is exactly one plane.
Pg. 23 |
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|
Term
| Theorem 1-3 Intersecting lines and planes |
|
Definition
If two lines intersect, then exactly one plane contains the lines.
Pg. 23 |
|
|
Term
If-Then Statements
Conditional Statements or conditionals |
|
Definition
Example:
If B is bewtween A and C, then AB + AC =AC
or
If p, then q
Pg. 33 |
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|
Term
|
Definition
The if part of an if-then statement
Pg. 33 |
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|
Term
|
Definition
The then part of an if-then statement
Pg. 33 |
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|
Term
|
Definition
When the hypothesis and conclusion are interchanged
Pg. 33 |
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|
Term
|
Definition
When an example can be found where the hypothesis is true and the conclusion is false.
Pg. 33 |
|
|
Term
|
Definition
When a conditional and is converse are both true they can be combined into a single statement.
A statement that contains the words "if and only if"
Pg. 34 |
|
|
Term
|
Definition
If a = b and c = d, then a + c = b +d
This can also be used to add a number to both sides.
Example: a + 2 = b + 2
Pg. 37 |
|
|
Term
|
Definition
If a = b and c =d, then a - c = b + d
This can also be used to subtract a number from both sides
Example: a - 2 = b - 2
Pg. 37 |
|
|
Term
|
Definition
If a = b and c = d, then a -c = b -d
This can also be used to multiply both sides of the equation by the same number.
Example: 1/2a = 1/2b
Pg. 37 |
|
|
Term
|
Definition
If a = b and c ≠ 0, then a/c = b/c
Pg. 37 |
|
|
Term
|
Definition
If a =b, then either a or b may be substituted for the other in any equation (or inequality)
Pg. 37 |
|
|
Term
|
Definition
|
|
Term
|
Definition
If a = b, then b = a
or
If < D ≅ < E, then < E ≅ < D
Pg. 37 |
|
|
Term
|
Definition
If a = b and b = c, then a =c
or
If < D ≅ < E and < E ≅ < F, the < D ≅ < F
Pg. 37 |
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|
Term
|
Definition
|
|
Term
|
Definition
If M is the midpoint of seg AB, then AM = 1/2AB and MB = 1/2AB
Pg. 43 |
|
|
Term
|
Definition
If Ray BX is the bisector of < ABC, then
m< ABX = 1/2m< ABC and m< XBC = 1/2m< ABC
Pg. 44 |
|
|
Term
|
Definition
Given Information
Definitions
Postulates
Properties of Equality or Congruency
Theorems (that have already been proved)
Pg. 45 |
|
|
Term
|
Definition
Two angles whose measures have the sum of 90
Each angle is called a complement of the other.
Pg. 50 |
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|
Term
|
Definition
Two angles whose measures have the sum of 180.
Each angle is called asupplement of the other.
Pg. 50 |
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|
Term
|
Definition
Two angles that have sides consisting of opposite rays. When two lines interest, they form two pairs of vertical angles.
Pg. 51 |
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|
Term
|
Definition
Vertical angles are Congruent
Pg. 51 |
|
|
Term
Theorem 2-4
If two lines are ┴, then ___________ |
|
Definition
If two lines are perpendicular, then they form congruent adjacent angles.
Pg. 56 |
|
|
Term
Theorem 2-5
If two lines form ≅ adj. <'s, then ________ |
|
Definition
If two lines form congruent adjacent angles, then the lines are perpendicular.
Pg. 56 |
|
|
Term
Theroem 2-6
If the ext. sides of two adj. actue <'s are ┴, then ________ |
|
Definition
If the exterior sides of two adjacent acute angles are perpendicular, then the angls are complementary.
Pg. 56 |
|
|
Term
|
Definition
Two lines that intersect to form right angles.
Pg. 56 |
|
|
Term
Theorem 2-7
Supplements of ≅ <'s |
|
Definition
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.
Pg. 61 |
|
|
Term
Theorem 2-8
Complements of ≅ <'s |
|
Definition
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.
Pg. 61 |
|
|
Term
Parrallel Lines
Parrallel Planes |
|
Definition
Are coplanar lines that do not intersect.
Planes that do not intersect
Pg. 73 |
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|
Term
|
Definition
Are noncoplanar lines, that are neither parallel or intersecting
Pg. 73 |
|
|
Term
A line and plane
are Parallel |
|
Definition
If they do not intersect
Pg. 73 |
|
|
Term
Theorem 3-1
If two ǁ planes are cut by a third plane, then _________ |
|
Definition
If two parallel planes are cut by a third plane, then the lines of intersection are parallel.
Pg. 74 |
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|
Term
|
Definition
A line that intersects two or more coplanar lines in different points.
Pg. 74 |
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|
Term
|
Definition
Two nonadjacent interior angles on opposite sides of the transversal.
Pg. 74 |
|
|
Term
Same-Side
Interior Angles |
|
Definition
Two interior angles on the same side of the transversal.
Pg. 74 |
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|
Term
|
Definition
Two angles in corresponding positions relative to the two lines.
Pg. 74 |
|
|
Term
Postulate 10
Correspoinding <'s |
|
Definition
If two parallel lines are cut by a transversal, then correspoinding angles are congruent.
Pg. 78 |
|
|
Term
Theorem 3-2
Starting with ǁ lines |
|
Definition
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
Pg. 78 |
|
|
Term
Theorem 3-3
Starting with ǁ lines |
|
Definition
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Pg. 79 |
|
|
Term
Theorem 3-4
If a transversal is ┴ to one of two ǁ lines, then _______ |
|
Definition
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.
Pg. 79 |
|
|
Term
Postulate 11
Converse to corr. <'s (Post. 10) |
|
Definition
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Pg. 83 |
|
|
Term
Theorem 3-5
Starting with alt. int. <'s |
|
Definition
If two lines are cut by a transversal and alt. int. angles are congruent, then the lines are parallel.
Pg. 83 |
|
|
Term
Theorem 3-6
Starting with same-side int. <'s |
|
Definition
If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.
Pg. 84 |
|
|
Term
|
Definition
In a plane two lines are perpendicular to the same line are parallel.
Pg. 84 |
|
|
Term
|
Definition
Through a point outside a line, there is exactly one line paralllel to the given line.
Pg. 85 |
|
|
Term
|
Definition
Through a point outside a line, there is exactly one line perpendicular to the given line.
Pg. 85 |
|
|
Term
Theorem 3-10
Three ǁ lines |
|
Definition
Two lines parallell to a third line are parallel to each other.
Pg. 85 |
|
|
Term
Ways to Prove
Two Lines Parallel |
|
Definition
Show corr. <'s are ≅
Show alt. int. <'s are ≅
Show same-side int. <'s are supp.
Show both lines are ┴ to a third line
Show both lines are ǁto a third line.
Pg. 85 |
|
|
Term
|
Definition
The figure formed by three segments joining three noncollinear points.
Pg. 93 |
|
|
Term
Vertex & Sides
of a triangle |
|
Definition
Vertex - each of the three points of the triangle (Pluural: Vertices)
Sides - The segments of a triangle
Pg. 93 |
|
|
Term
|
Definition
|
|
Term
|
Definition
At least two sides congruent
Pg. 93 |
|
|
Term
|
Definition
All sides congruent
Can also be considered isosceles
Equilateral triangle is also equiangular
Pg. 93 |
|
|
Term
|
Definition
|
|
Term
|
Definition
One obtues <
A triangle can not have more then one obtuse <
Pg. 93 |
|
|
Term
|
Definition
One right <
A triangle can not have more than one right <
Pg. 93 |
|
|
Term
|
Definition
All <'s congruent
Equiangular triangles are also equilaterial
Pg. 93 |
|
|
Term
Theorem 3-11
Sum of the int. <'s of a ∆ |
|
Definition
The sum of the measure of the angles of a triangle is 180
Pg. 94 |
|
|
Term
Corollary 1, 2, 3 & 4
of Theorem 3-11 |
|
Definition
1. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent
2. Each angle of an equiangular triangle has measure 60
3. In a triangle, there can be at most one right angle or obtuse angle
4. The acute angles of a right triangle are complementary.
Pg. 94 |
|
|
Term
Theorem 3-12
Ext. < of a ∆ |
|
Definition
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
Pg. 95 |
|
|
Term
|
Definition
A line, ray, or segement added to a diagram to help in a proof.
Pg. 94 |
|
|
Term
|
Definition
Means "many angles". Any figure with three or more sides having the two qualitiles below.
1. Each segment intersects exactly two other segements, one at each endpoint
2. No two segments with a common endpoints are collinear
Pg. 101 |
|
|
Term
|
Definition
A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
Pg. 101 |
|
|
Term
|
Definition
3 Triangle 4 Quadrilateral
5 Pentagon 6 Hexagon
8 Octagon 10 Decagon
n n-gon
Pg. 101 |
|
|
Term
|
Definition
A segment joining two nonconsecutive vertices of a polygon.
Pg. 102 |
|
|
Term
Theorem 3-13
Sum of int. <'s of a polygon |
|
Definition
The sum of the measures of the angles of a convex polygon with n sides is (n-2)180
Pg. 102 |
|
|
Term
Theorem 3-14
Sum of ext. <'s of a polygon |
|
Definition
The sume of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.
Pg. 102 |
|
|
Term
|
Definition
A polygon that is both equiangluar and equlateral.
Pg. 103 |
|
|
Term
|
Definition
Conclusion based on accepted statements (definitions, postulates, previous theorems, corolaries, and given information)
Conclusion must be true if hypotheses are true.
Pg. 106 |
|
|
Term
|
Definition
Conclusion based on several past observations
Conclusion is probably true, but not necessarily true.
Pg. 106 |
|
|
Term
|
Definition
When two figures have the same size and shape.
Pg. 117 |
|
|
Term
|
Definition
When two shapes are ≅, then each < and side of one shape with correspond to an < and side of the other shape.
Pg. 117 - 118 |
|
|
Term
|
Definition
Corresponding parts of ≅ ∆s are ≅
Used after a polygon is shown ≅ to another polygon.
Pg. 118 |
|
|
Term
|
Definition
Side Side Side Postulate
If three sides of one ∆ are ≅ to three sides of another ∆ then the ∆s are ≅
Pg. 122 |
|
|
Term
|
Definition
Side Angle Side Psotulate
If two sides and the included < of one ∆ are ≅ to two sides and the included < of anther ∆, then the ∆s are ≅
Pg. 122 |
|
|
Term
|
Definition
Angle Side Angle Postulate
If two <s and the included side of one ∆ are ≅ to two <s and the included side of anther ∆, then the ∆s are ≅
Pg. 123 |
|
|
Term
| A line and a plane are ┴ IF |
|
Definition
If and Only If they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection.
Pg. 128 |
|
|
Term
| How to Prove Segments or <s ≅ |
|
Definition
1. Identify two ∆s in which the two segments or <s are corresponding parts.
2. Prove that the triangles are ≅
3. State that the two parts are ≅, using CPCT
Pg. 129 |
|
|
Term
Legs & Base
of an Isosceles ∆ |
|
Definition
*The legs of an isosceles ∆ are the ≅ sides.
*The base is the third side.
*The <s along the base are called base <s
*The < opp. the base is the vertex angle.
Pg. 134 |
|
|
Term
|
Definition
If two sides of a ∆ are ≅, then the <s opposite those sides are ≅.
Pg. 135 |
|
|
Term
Corollary 1, 2, & 3
of Isosceles ∆ Theorem |
|
Definition
1. An equilateral ∆ is also equiangluar
2. An equilateral ∆ has three 60⁰ <
3. The bisector of the vertex < of an isosceles ∆ is ┴ to the base at its midpoint.
Pg. 135 |
|
|
Term
Theorem 4-2
Converse of Isosceles ∆ Theorem |
|
Definition
If two <s of a ∆ are ≅, then the sides opposite those <s are ≅
Pg. 136 |
|
|
Term
Corollary 1
of Theorem 4-2 |
|
Definition
An equiangluar ∆ is also equilateral
Pg. 136 |
|
|
Term
|
Definition
Angle Angle Side Theorem
If two <s and a non-included side of one ∆ are ≅ to the corresponding parts of anther ∆, then the ∆s are ≅
Pg. 140 |
|
|
Term
Hypotenuse & Legs
of a Right ∆ |
|
Definition
Hypotenuse (hyp.)- the side opposite the right <
Legs - are the other two side or the ┴ sides
Pg. 141 |
|
|
Term
|
Definition
Hypotenuse Leg Theorem
If the hypotenuse and a leg of one right ∆ are ≅ to the corresponding parts of another ∆, then the ∆s are ≅
Pg. 141 |
|
|
Term
|
Definition
All ∆: SSS SAS ASA AAS
Right ∆: HL
Pg. 141 |
|
|
Term
|
Definition
A segment from a vertex to the midpoint of the opposite side.
Pg. 152 |
|
|
Term
|
Definition
A ┴ segment from a vertex to the line that contains the opposite side Pg. 152
*Acute ∆s have all three altitudes inside the ∆
*Right ∆s have two altitudes as legs and the other inside the ∆
*Obtuse ∆s have two altitudes outside and one inside the ∆ |
|
|
Term
|
Definition
A segment that is ┴ to another segment at its midpoint
*The segment is both the altitude and median
Pg. 153 |
|
|
Term
Theorem 4-5
Starting with perp. bis |
|
Definition
If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.
Pg. 153 |
|
|
Term
Theorem 4-6
Starting with point equidistant from endpts. |
|
Definition
If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
Pg. 153 |
|
|
Term
Distance From
a Point to a Line |
|
Definition
The length of the ┴ segment from the point to the line or plane.
*Important for theorem 4-7 and 4-8
Pg. 154 |
|
|
Term
Theorem 4-7
Starting with < bis. |
|
Definition
If a point lies on the bisector of an <, then the point is equidistant from the sides of the <.
Pg. 154 |
|
|
Term
Theorem 4-8
Starting with pt. equidistant from sides of an < |
|
Definition
If a point is equidistant from the sides of an <, then the point lies on the bisector of the <.
Pg. 154 |
|
|
Term
|
Definition
A quad. with both pairs of opposite sides ǁ (Usually shown by a tilted rectangle.)
Pg. 167 |
|
|
Term
Theorem 5-1
Opp. sides of a parallelogram |
|
Definition
Opposite sides of a parallelogram are ≅
Pg. 167 |
|
|
Term
Theorem 5-2
Opp. <s of a parallelogram |
|
Definition
Opposite <s of a parallelogram are ≅
Pg. 167 |
|
|
Term
Theorem 5-3
Diagonals of a parallelogram |
|
Definition
Diagonals of a parallelogram bisect each other.
Pg. 167 |
|
|
Term
Theorem 5-4
Starting with both pairs of opp. sides of a quad. ≅ |
|
Definition
If both pairs of opposite sides of a quad. are ≅, then the quad. is a parallelogram
Pg. 172 |
|
|
Term
Theorem 5-5
Starting with one pair of opp. sides of a quad. both ≅ and ǁ |
|
Definition
If one pair of opp. sides of a quad. are both ≅ and ǁ, then the quad. is a parallelogram.
Pg. 172 |
|
|
Term
Theorem 5-6
Starting with both pairs of opp. sides of a quad. ≅ |
|
Definition
If both pairs of opp. <s of a quad. are ≅, then the quad. is a parallelogram.
Pg. 172 |
|
|
Term
Theorem 5-7
Starting with diagonals of a quad bisect each other |
|
Definition
If the diagonals of a quad. bisect each other, then the quad. is a parallelogram.
Pg. 172 |
|
|
Term
| Five Ways to Prove a Quad is a Parrallelogram |
|
Definition
1. Show both pairs of opp. sides ǁ
2. Show both pairs of opp. sides ≅
3. Show one pair opp. Sides ≅ and ǁ
4. Show both pairs opp. <s ≅
5. Show diagonals bisect each other
Pg. 172 |
|
|
Term
Theorem 5-8
Starting with ǁ lines |
|
Definition
If two lines are ǁ, then all points on one line are equidistant from the other line.
Pg. 177 |
|
|
Term
Theorem 5-9
ǁ lines and ≅ segments |
|
Definition
If three ǁ lines cut off ≅ segments on one transversal, then they cut off ≅ segments on every transversal.
Pg. 177 |
|
|
Term
Theorem 5-10
Midpoint of a side of a ∆ and ǁ lines |
|
Definition
A line that contains the midpoint of one side of a ∆ and is ǁ to another side passes through the midpoint of the third side.
Pg. 178 |
|
|
Term
Theorem 5-11
Joining midpoints of two sides of a ∆ |
|
Definition
The segment that joins the midpoints of two sides of a ∆
1. is ǁ to the third side
2. is half as long as the third side
Pg. 178 |
|
|
Term
|
Definition
A quad. with four right <s
Pg. 184 |
|
|
Term
|
Definition
A quad. with four ≅ sides (Diamond)
Pg. 184 |
|
|
Term
|
Definition
A quad. with four right <s and four ≅ sides
*This could be called a rectangle or a rhombus
Pg. 184 |
|
|
Term
Theorem 5-12
Diagonals of a Rectangle |
|
Definition
The diagonals of a rectangle are ≅
Pg. 185 |
|
|
Term
Theorem 5-12
Diagonals of a rhombus |
|
Definition
The diagonals of a rhombus are ┴
Pg. 185 |
|
|
Term
Theorem 5-14
Diagonals and <s of a rhombus |
|
Definition
Each diagonal of a rhombus bisects two <s of the rhombus.
Pg. 185 |
|
|
Term
Theorem 5-15
Midpoint of the hyp. of a right ∆ |
|
Definition
The midpoint of the hyp. of a right ∆ is equidistant from the three vertices.
Pg. 185 |
|
|
Term
Theorem 5-16
Parallelogram and rt. < |
|
Definition
If an < of a parallelogram is a right <, then the parallelogram is a rectangle.
Pg. 185 |
|
|
Term
Theorem 5-17
Consecutive sides ≅ |
|
Definition
If two consecutive sides of a parallelogram are ≅, then the parallelogram is a rhombus.
Pg. 185 |
|
|
Term
|
Definition
A quad. with exactly one pair of ǁ sides
Pg. 190 |
|
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Term
Base & Legs
of a trapezoid |
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Definition
Bases- ǁ sides of the trapezoid
Legs- the other two sides
Pg. 190 |
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Term
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Definition
A trapezoid with ≅ legs
Pg. 190 |
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Term
Theorem 5-18
Base <s of an isosceles trapezoid |
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Definition
Theorem 5-18
Base <s of an isosceles trapezoid are ≅
Pg. 190 |
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Term
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Definition
The segment that joins the midpoints of the legs.
Pg. 191 |
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Term
Theorem 5-19
Median of a trapezoid |
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Definition
The median of a trapezoid
1. is ǁ to the bases
2. has a length equal to the average of the base lengths
Pg. 191 |
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Term
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Definition
If a > b and c ≥ d, then a + c > b + d
If a > b and c > 0, then ac > bc and a/c > b/c
If a > b and c < 0, then ac < bc and a/c < b/c
If a > b and b > c, then a > c
If a = b + c and c > 0, then a > b
Pg. 204 |
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Term
Theorem 6-1
The Ext. < Inequality
Theorem |
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Definition
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
Pg. 204 |
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Term
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Definition
Given Statement: If p, then q
Contrapositive: If not q, then not p
Converse: If q, then p
Inverse: If not p, then not q
Pg. 208 |
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Term
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Definition
When the same venn diagram represents both a conditional and it contrapositive.
Pg. 208 |
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Term
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Definition
Begin by assuming temporarily that the desired conclusion is not true. Then you reason logically until you reach a contradiction of the hypothesis or some other known fact. Because you've reached a contradiction, you know that the temporary assumption is impossible and therefore the desired conclusion must be true.
Pg. 214 |
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Term
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Definition
If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.
Pg. 219 |
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Term
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Definition
If one < of a triangle is larger than a second <, then the side opposite the first < is longer than the side opposite the second <.
Pg. 220 |
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Term
Corollary 1 and 2
of Theorem 6-3 |
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Definition
Corollary 1 - The perpendicular segment from a point to a line is the shortest segment from the point to the line.
Corollary 2 - The perpendicular segment from a point to a plane is the shoretest segment from the point to the plane.
Pg. 220 |
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Term
Theorem 6-4
The Triangle Inequality |
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Definition
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Pg. 220 |
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Term
Theorem 6-5
SAS Inequality Theorem |
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Definition
If two sides of one triangle are congruent to two sides of another triangle, but the included < of the first triangle is larger than the included < of te second, then the third side of the first triangle is longer than the third side of the second triangle.
Pg. 228 |
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Term
Theorem 6-6
SSS Inequality Theorem |
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Definition
If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included < of the first triangle is larger than the included < of the second.
Pg. 229 |
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Term
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Definition
The quotient when the first number is divided by the second
The ratio of 8 to 12 is 8/12 or 2/3
Pg. 241 |
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Term
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Definition
An equation stating that two ratios are equal
a/b = c/d and a:b = c:d
Pg. 242 |
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Term
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Definition
The first and last term of a proportion are called the extremes. The middle terms are the means.
a:b = c:d 6:9 = 2:3 6/9 = 2/3
a, c, 6, & 3 are the Extremes
b,c,9, & 2 are the means
Pg. 245 |
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Term
| Properties of Proportions |
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Definition
1. a/b =c/d is Equivalent to:
a. ad = bc
b. a/c = b/d
c. b/a = d/c
d. (a+b)/b = (c+d)/d
2. If a/b = c/d = e/f = …., then (a+c+e+…)/(b+d+f+….) = a/b = ...
Pg. 245 |
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Term
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Definition
Two polygons are similar if their vertices can be paired so that:
1. Corresonding <s are ≅
2. Corresponding sides are in porportion (Their lengths have the same ratio)
Pg. 249 |
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Term
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Definition
The ratio of the lengths of two corresponding sides of two similar polygons.
Pg. 249 |
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Term
Postulate 15
AA Similarity |
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Definition
If two <s of one Δ are ≅ to two <s of another Δ, then the Δ's are similar.
Pg. 255 |
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Term
Theorem 7-1
SAS Similarity |
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Definition
If an < of one Δ is ≅ to an < of another Δ and the sides including those <s are in proportion, then the Δ's are similar.
Pg. 263 |
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Term
Theorem 7-2
SSS Similarity |
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Definition
If the sides of two Δ's are in proportion, then the Δ's are similar.
Pg. 263 |
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Term
Theorem 7-3
Δ Proportionality |
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Definition
If a line II to one side of a Δ intersects the other two sides, then it divides those sides proportionally.
Pg. 269 |
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Term
Corollary 1
of Theorem 7-3 |
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Definition
If three II lines interest two transversals, then they divide the transversals, proportionally.
Pg. 270 |
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Term
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Definition
If a ray bisects an < of a Δ, then it divides the opposite side into segments proportional to the other two sides.
Pg. 270 |
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