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58 Terms
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1
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Perpendicular Bisector
A line that forms 90 degree angles and cuts a segment in half. Any point on the perpendicular bisector is equidistant to the endpoints of the segment.
2
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Angle Bisector
A ray or line that cuts an angle in half. Any point on the angle bisector is equidistant to the sides of the angle.
3
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Line of Symmetry
A line that divides a figure into two equal reflections of each other. If you fold the figure over this line, it will lie exactly on top of itself.
4
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Corresponding parts of congruent triangles are congruent (CPCTC)
A theorem stating that if two triangles are congruent, then so are all corresponding parts.
5
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Congruent Sides
Sides that have the exact same length.
6
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Vertex of an Angle
The vertex is where the two rays that form the angle meet.
7
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Corresponding Sides
Two sides that are situated the same way in different objects (in red).
8
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Corresponding Angles
Two angles that are situated the same way in different objects (e.g., angles E and G)
9
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Third Angle Theorem
If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent
10
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Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
11
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Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite of the angles are congruent.
12
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Congruent
When two parts of a geometric figure have the same shape and size.
13
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Corresponding
Basic geometric figures that are in the same position in different shapes.
14
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Included side
A side that is between two angles in a triangle
15
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In the figure, LM is the included side between angle L and angle M.
16
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Included angle
An angle that is between two sides in a triangle
17
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In the figure, angle N is the included angle between LN and MN.
18
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Angle-Angle-Angle (AAA)
AAA does NOT prove triangles congruent; DOES show that triangles are SIMILAR.
19
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Side-Side-Angle (SSA)
SSA does NOT prove triangles congruent - do not use!!
20
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Congruent Triangles
3 pairs of corresponding angles are congruent and 3 pairs of corresponding sides are congruent.
21
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Equiangular Triangle
A triangle whose angles are all congruent.
22
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Scalene Triangle
A triangle that has no congruent sides.
23
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Isosceles Triangle
A triangle with at least two congruent sides.
24
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Equilateral Triangle
A triangle that has all three sides congruent.
25
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Triangle Sum Theorem
The sum of the measures in a triangle is 180 degrees.
26
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Exterior Angle Theorem
The sum of the remote interior angles is equal to the measure of the exterior angle.
27
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Reflexive property
A shape is congruent (equal) to itself. Shapes can be used in more than one figure. Segment RS is used in the red and blue triangles.
28
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Triangle rigidity
If the side lengths of a triangle are given, the triangle can only have one shape.
29
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congruent shapes
two figures that have corresponding congruent sides and angle measures (same exact size and shape)
30
New cards
Perpendicular Bisector
A line that forms 90 degree angles and cuts a segment in half. Any point on the perpendicular bisector is equidistant to the endpoints of the segment.
31
New cards
Angle Bisector
A ray or line that cuts an angle in half. Any point on the angle bisector is equidistant to the sides of the angle.
32
New cards
Line of Symmetry
A line that divides a figure into two equal reflections of each other. If you fold the figure over this line, it will lie exactly on top of itself.
33
New cards
Corresponding parts of congruent triangles are congruent (CPCTC)
A theorem stating that if two triangles are congruent, then so are all corresponding parts.
34
New cards
Congruent Sides
Sides that have the exact same length.
35
New cards
Vertex of an Angle
The vertex is where the two rays that form the angle meet.
36
New cards
Corresponding Sides
Two sides that are situated the same way in different objects (in red).
37
New cards
Corresponding Angles
Two angles that are situated the same way in different objects (e.g., angles E and G)
38
New cards
Third Angle Theorem
If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent
39
New cards
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
40
New cards
Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite of the angles are congruent.
41
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Congruent
When two parts of a geometric figure have the same shape and size.
42
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Corresponding
Basic geometric figures that are in the same position in different shapes.
43
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Included side
A side that is between two angles in a triangle
44
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In the figure, LM is the included side between angle L and angle M.
45
New cards
Included angle
An angle that is between two sides in a triangle
46
New cards
In the figure, angle N is the included angle between LN and MN.
47
New cards
Angle-Angle-Angle (AAA)
AAA does NOT prove triangles congruent; DOES show that triangles are SIMILAR.
48
New cards
Side-Side-Angle (SSA)
SSA does NOT prove triangles congruent - do not use!!
49
New cards
Congruent Triangles
3 pairs of corresponding angles are congruent and 3 pairs of corresponding sides are congruent.
50
New cards
Equiangular Triangle
A triangle whose angles are all congruent.
51
New cards
Scalene Triangle
A triangle that has no congruent sides.
52
New cards
Isosceles Triangle
A triangle with at least two congruent sides.
53
New cards
Equilateral Triangle
A triangle that has all three sides congruent.
54
New cards
Triangle Sum Theorem
The sum of the measures in a triangle is 180 degrees.
55
New cards
Exterior Angle Theorem
The sum of the remote interior angles is equal to the measure of the exterior angle.
56
New cards
Reflexive property
A shape is congruent (equal) to itself. Shapes can be used in more than one figure. Segment RS is used in the red and blue triangles.
57
New cards
Triangle rigidity
If the side lengths of a triangle are given, the triangle can only have one shape.
58
New cards
congruent shapes
two figures that have corresponding congruent sides and angle measures (same exact size and shape)
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