Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

Geometry💀 > Proof definitions, postulates and theorems > Flashcards

Proof definitions, postulates and theorems Flashcards

(69 cards)

Start Studying
1
Q

Addition Poe

A

If a = b, then

a+c=b+c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Perpendicular Lines

A

Meet at a right angle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Equilateral

A

A polygon where all sides are congruent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Equiangular

A

All angles are congruent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Subtraction Poe

A

If a = b, then

a-c=b-c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Multiplication Poe

A

If a = b, then

a(c)=b(c)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Division Poe

A

If a = b, then

a/c=b/c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Substitution Poe

A

If a = b, then

“a” can be substituted for “b” in any expression

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Distributive Poe

A

If a = b, then

a(b+c)+ab+ac

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Reflexive Poe

A

Basically, a thing equals itself

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Symmetric Poe

A

Basically, if one expression equals another it doesn’t matter which expression goes on which side.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Transitive Poe

A

Basically, if two things equal a third thing, they also equal each other

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Reflexive Poc

A

Basically, a thing(angle or side) is congruent to itself

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Symmetric Poc

A

Basically, if one thing(angle or side) equals another it doesn’t matter which thing goes on which side

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Transitive Poc

A

Basically, if two thing(angle or side) equal a third thing, they also equal each other

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Right Angles Congruence Theorem

A

All right angles are congruent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Vertical Angles Congruence Theorem

A

All vertical angles are congruent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Linear Pair Postulate

A

Angles in a linear pair are supplements

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Congruent Complements Theorem

A

If two angles are complementary to the same angle, they are congruent to each other

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Congruent Complements Theorem

A

If two angles are supplementary to the same angle, they are congruent to each other

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Parallel Postulate

A

given a line and a point not on the line, you can draw only one line that is parallel to the original line and goes through the point

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Perpendicular Postulate

A

given a line and a point not on the line, you can draw only one line that is perpendicular to the original line and goes through the point

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Transversal

A

a line that intersects two or more other lines at different points

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Consecutive Interior Angles

A

Angles inside the lines and on the same side of the transversal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Alternate Interior Angles
Angles inside the lines and on opposite sides of the transversal
26
Alternate Exterior Angles
Angles outside the lines and opposite of the transversal
27
Corresponding Angles
Same corner of different intersections
28
Consecutive Interior Angles Postulate
For parallel lines crossed by a transversal, interior angles are supplementary
29
Alternate Interior Angles Postulate
For parallel lines crossed by a transversal, alternate interior angles are congruent
30
Alternate Exterior Angles Postulate
For parallel lines crossed by a transversal, alternate exterior angles are congruent
31
Corresponding Angles Postulate
For parallel lines crossed by a transversal, corresponding angles are congruent
32
If parallel lines are cut by a transversal...
- Consecutive interior angles are supplementary | - Alternate interior, alternate exterior and corresponding angles are congruent
33
Consecutive Interior Angles Converse Theorem
For lines cut by a transversal, if their consecutive interior angles are congruent then the lines are parallel
34
Alternate Interior Angles Converse Theorem
For lines cut by a transversal, if their alternate interior angles are congruent then the lines are parallel
35
Alternate Exterior Angles Converse Theorem
For lines cut by a transversal, if their alternate exterior angles are congruent then the lines are parallel
36
Corresponding Angles Converse Theorem
For lines cut by a transversal, if their corresponding angles are congruent then the lines are parallel
37
Transitive Property of Parallel Lines
If a is parallel to b and b is parallel to c, then a is parallel to c
38
Linear Pair Perpendicular Theorem
If two lines intersect to form a pair of congruent angles, then the lines are perpendicular
39
"Four Right Angles" Theorem
If two lines are perpendicular, then they intersect to form 4 right angles
40
"Perpendicular Sides Complementary Angles" Theorem
If two sides of two adjacent angles are perpendicular, then the angles are complementary
41
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other
42
Lines perpendicular to the Transversal Theorem
In a plane if two lines are perpendicular to the same lines, then they are parallel to each other
43
Triangle Sum Theorem
The angles of a triangle add up to 180 degrees
44
Exterior Angles Theorem
The measure of an exterior angle equals the sum of the remote interior angle(the two interior angles NOT adjacent to the exterior angle)
45
Definition of Congruent Triangles
If two triangles have 3 pairs of congruent corresponding angles and 3 pairs of congruent corresponding sides, the triangles are congruent
46
CPCTC
Corresponding parts of congruent triangles are congruent
47
SSS Postulate
If two triangles have 3 pairs of congruent corresponding sides, then the triangles are congruent
48
SAS Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the two triangles are congruent
49
Hypotenuse Leg Congruence Postulate
If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the triangles are congruent
50
ASA Postulate
If two angles and the included side(side in between two angles) of two triangles are congruent then the triangles are congruent
51
AAS Postulate
If two angles and a non included side of two triangles are congruent then the triangles are congruent
52
Base Angle Theorem
If two sides of triangles are congruent, then the angles opposite from them are congruent
53
Converse of Base Angle Theorem
If two angles of a triangle are congruent, then the sides opposite from them are congruent
54
Corollaries to Base Angle Theorem
If a triangle is equilateral, it is equiangular and if a triangle is equiangular, it is equilateral
55
Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle(the midsegment) is parallel to and half as long as the third side
56
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
57
Converse of Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment,, it is on the perpendicular bisector of a segment
58
Angle Bisector Theorem
If a point is on the angle bisector of an angle then it is equidistant from the two sides of the angle
59
Converse of Angle Bisector Theorem
If a point inside an angle is equidistant from the two sides of the angle then it is on the angle bisector
60
Altitude
A line segment that connects a vertex of a triangle with the opposite side and is perp to that side
61
Median
A line segment that connects a vertex of a triangle with the midpoint of the opposite side
62
Triangle Inequality Theorem
Basically, if the third side is too short or too long, we end up with a line and not a triangle
63
"All Lengths are Similar" Theorem
If two shapes are similar, all of their length-related measures are the same ratio as the scale factor
64
AA Similarity Postulate
if two sets of corresponding angles of triangles are congruent, then the triangles are similar
65
SSS Similarity Theorem
If the ratios of three pairs of corresponding sides are equal, then the triangles are similar
66
SAS Similarity Postulate
If the ratio of two pairs of corresponding sides are equal AND the included angles are congruent, then the triangles are simialr
67
Side Splitter Theorem
If a line parallel to one side of a triangle intersects the two other sides, then it divides the sides proportionally
68
Extension of Side Splitter Theorem
If three parallel lines intersect two transversals then they divide the transversals proportionally
69
Angle Bisector Theorem(for triangles)
If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to their adjacent sides

Geometry💀 (2 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions