Geometry Postulates And Theorems

Front 1

Through any 2 points ________

Back 1

there exists one line.

Front 2

A line contains ______

Back 2

at least 2 points.

Front 3

If two lines intersect, _____

Back 3

then their intersection is exactly one point.

Front 4

Through any three noncollinear points _____

Back 4

there exists exactly one plane.

Front 5

A plane contains ____

Back 5

at least three noncollinear points.

Front 6

If two points lie in a plane, ____

Back 6

then the line containing them lies in the plane.

Front 7

If two planes intersect, ____

Back 7

then their intersection is a line.

Front 8

If two angles from a linear pair,____

Back 8

then they are supplementary.
Linear Pair Postulate

Front 9

If there is a line and a point not on the line,_____

Back 9

then there is exactly one line through the point parallel/perpendicular to the given line.
Parallel/Perpendicular Postulate

Front 10

If two parallel lines are cut by a transversal,_____

Back 10

then the corresponding angles-
/AIA/AEA/slopes are congruent, CIA are supplementary
Corresponding Angles Postulate

Front 11

If two lines are cut by a transversal like the corresponding angles-/AIA/AEA/slopes are congruent, CIA are supplementary__

Back 11

then the lines are parallel
Corresponding Angles Converse

Front 12

In a coordinate plane, two nonvertical lines are parallel if and only if____

Back 12

they have the same slope. Any two vertical lines are parallel.
Slopes of Parallel Lines

Front 13

In a coordinate plane, two nonvertical lines are perpendicular if and only if___

Back 13

the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
Slopes of Perpendicular Lines

Front 14

SSS Congruence Postulate

Back 14

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Front 15

SAS Congruence Postulate

Back 15

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangle are congruent.

Front 16

ASA Congruence Postulate

Back 16

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

Front 17

All right angles___

Back 17

are congruent.
Right Angle Congruence Theorem

Front 18

If two angles are supplementary to the same angle___

Back 18

then they are congruent.
Congruent Supplements Theorem

Front 19

If two angles are complementary to the same angle_____

Back 19

then the two angles are congruent.
Congruent Complements Theorem

Front 20

Vertical Angles Theorem

Back 20

Vertical angles are congruent.

Front 21

If two lines intersect to form a linear pair of congruent angles,___

Back 21

then the lines are perpendicular.

Front 22

If two sides of two adjacent acute angles are perpendicular,___

Back 22

then the angles are complementary.

Front 23

If a transversal is perpendicular to one of two parallel lines,_____

Back 23

then it is perpendicular to the other.
Perpendicular Transversal

Front 24

If two lines are parallel to the same line,___

Back 24

then they are parallel to each other.

Front 25

In a plane, if two lines are perpendicular to the same line,___

Back 25

then they are parallel to each other.

Front 26

The sum of the measures of the interior angles of a triangle___

Back 26

is 180 degrees.
Triangle Sum Theorem

Front 27

The measure of an exterior angle of a triangle____

Back 27

is equal to the sum of the measures of the two nonadjacent interior angles.
Exterior Angle Theorem

Front 28

The acute angles of a right triangle____

Back 28

are complementary.
Corolary

Front 29

If two angles of one triangle are congruent to two angle of another triangle_____

Back 29

then the third angles are also congruent.
Third Angles Theorem

Front 30

AAS Congruence Theorem

Back 30

If two angles and nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.

Front 31

If two sides of a triangle are congruent,_____

Back 31

then the angles opposite them are congruent.
Base Angles Theorem

Front 32

If a triangle is equilateral,____

Back 32

then it is equiangular.
Corollary

Front 33

If a triangle is equiangular____

Back 33

then it is equilateral.
Corollary

Front 34

If two angles of a triangle are congruent,____

Back 34

then the sides opposite them are congruent.
Converse Base Angles Theorem

Front 35

HL Congruence Theorem

Back 35

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two angles are congruent.

Front 36

if a=b, then c-a=c-b

Back 36

Subtraction Property

Front 37

if a=b, then ca=cb where c does not = 0

Back 37

Multiplication Property

Front 38

if a=b, then c+a=c+b

Back 38

Addition Property

Front 39

if a=b, then c/a=c/b where a,b, and c does not = 0

Back 39

Division Property

Front 40

a(b+c)=ab+ac

Back 40

Distributive Property

Front 41

x=x

Back 41

Reflexive Property

Front 42

if a=b and b=c than a=c

Back 42

Transitive Property

Front 43

(a+b)+c=a+(b+c)

Back 43

Associative Property

Front 44

a+b+c=c+a+b

Back 44

Communitive Property

Front 45

if a=b the a can replace b

Back 45

Substitution Property

Front 46

if a=b then b=a

Back 46

Symmetric Property