Geometry Postulate And Theorem Flashcards (Not Fully Completed,check Back Soon For A Full List)

Front 1

Segment Addition Postulate

Back 1

If B is between A and C,then AB+BC=AC. If AB+BC=AC, then B is between A and C.

Front 2

Angle Addition Postulate

Back 2

If P is in the interior of ∠RST, then m∠RSP+m∠PST=m∠RST.

Front 3

N/A

Back 3

Through any two points there exists exactly one line.

Front 4

N/A

Back 4

A line contains at least two points.

Front 5

N/A

Back 5

If two lines intersect, then their intersection is exactly one point.

Front 6

N/A

Back 6

Through any three noncollinear points there exists exactly one plane.

Front 7

N/A

Back 7

A plane contains at least three noncollinear points.

Front 8

N/A

Back 8

If two points lie in a plane, then the line containing them lies in the plane.

Front 9

N/A

Back 9

If two planes intersect, then their intersection is a line.

Front 10

Linear Pair Postulate

Back 10

If two angles form a linear pair, then they are supplementary.

Front 11

Parallel Postulate

Back 11

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Front 12

Perpendicular Postulate

Back 12

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Front 13

Corresponding Angles Postulate

Back 13

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Front 14

Corresponding Angles Converse

Back 14

If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

Front 15

Slopes of Parallel Lines

Back 15

In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.

Front 16

Slopes of Perpendicular Lines

Back 16

In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.

Front 17

Side-Side-Side Congruence Postulate

Back 17

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

Front 18

Side-Angle-Side Congruence Postulate

Back 18

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

Front 19

Angles-Side-Angle Congruence Postulate

Back 19

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 20

Area of a Square Postulate

Back 20

The area of a square is the square of the length of its side, or A=s².

Front 21

Area Congruence Postulate

Back 21

If two polygons are congruent,then they have the same area.

Front 22

Area Addition Postulate

Back 22

The area of a region is the sum of the areas of its nonoverlapping parts.

Front 23

Angle-Angle Similarity Postulate

Back 23

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Front 24

Arc Addition Postulate

Back 24

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Front 25

Volume of a Cube

Back 25

The volume of a cube is the cube of the length of its side.

Front 26

Volume Congruence Postulate

Back 26

If two polyhedra are congruent, then they have the same volume.

Front 27

Volume Addition Postulate

Back 27

The volume of a solid is the sum of the volumes of all its nonoverlapping parts.

Front 28

Properties of Segment Congruence

Back 28

Segment congruence is reflexive, symmetric, and transitive.

Front 29

Properties of Angle Congruence

Back 29

Angle congruence is reflexive, symmetric, and transitive.

Front 30

Right Angle Congruence Theorem

Back 30

All right angles are congruent.

Front 31

Congruent Supplements Theorem

Back 31

If two angles are supplementary to the same angle then they are congruent.

Front 32

Congruent Supplements Theorem

Back 32

If two angles are complementary to the same angle then the two angles are congruent.

Front 33

Vertical Angles Theorem

Back 33

Vertical angles are congruent.

Front 34

N/A

Back 34

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

Front 35

N/A

Back 35

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Front 36

N/A

Back 36

If two lines are perpendicular, then they intersect to form four right angles.

Front 37

Alternate Interior Angles

Back 37

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Front 38

Consecutive Interior Angles

Back 38

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Front 39

Alternate Exterior Angles

Back 39

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Front 40

Perpendicular Transversal

Back 40

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Front 41

Alternate Interior Angles Converse

Back 41

If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

Front 42

Consecutive Interior Angles Converse

Back 42

If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

Front 43

Alternate Interior Angle Converse

Back 43

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

Front 44

N/A

Back 44

If two lines are parallel to the same line, then they are parallel to each other.

Front 45

N/A

Back 45

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Front 46

Triangle Sum Theorem

Back 46

The sum of the measures of the interior angles of a triangle is 180°.

Front 47

Exterior Angle Theorem

Back 47

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Front 48

Third Angles Theorem

Back 48

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Front 49

Reflexive Property of Congruent Triangles

Back 49

Every triangle is congruent to itself.

Front 50

Symmetric Property of Congruent Triangles

Back 50

If △ABC congruent △DEF, then △DEF congruent △ABC

Front 51

Transitive Property of Congruent Triangles

Back 51

If △ABC congruent △DEF and △DEF congruent △JKL, then △ABC congruent △JKL.