Geometry Grade 9

Front 1

Corresponding Angles Postulate

Back 1

If a transversal intersects two parallel lines then the corresponding angles are congruent

Front 2

Alternate Interior Angles Theorem

Back 2

If a transversal intersects two parallel lines, then alternate interior angles are congruent

Front 3

Same-Side Interior Angle Theorem

Back 3

If a transversal intersects two parallel then same-side interior angles are supplementary

Front 4

Alternate Exterior Angles Theorem

Back 4

If a transversal intersects two parallel then alternate exterior angles are congruent

Front 5

Same-Side Exterior Angles Theorem

Back 5

If a transversal intersects two parallel then same-side exterior angles are supplementary

Front 6

Converse of the Corresponding Angles Postulate

Back 6

If two lines and a transversal form corresponding angles that are congruent, then the 2 lines are parallel

Front 7

Converse of the Alternate Interior Angles Theorem

Back 7

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

Front 8

Converse of the Same-Side Interior Angles Theorem

Back 8

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel

Front 9

Converse of the Alternate Exterior Angles Theorem

Back 9

If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel

Front 10

Converse of the Same-Side Exterior Angles Theorem

Back 10

If two lines and a transversal form same side exterior angles that are supplmentary, then the lines are parallel

Front 11

Parallel & Perpendicular Lines
Theorem 3-9

Back 11

If 2 lines are parallel to the same line, then they are parallel to each other

Front 12

Theorem 3-10

Back 12

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

Front 13

Theorem 3-11

Back 13

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other

Front 14

Triangle Angle-Sum Theorem

Back 14

The sum of the measures of the angles of a triangle is 180

Front 15

Triangle Exterior Angle Theorem

Back 15

The measure of each exterior angle of a triangle equals the sum of the measures of its 2 remote interior angles

Front 16

Corollary

Back 16

The measure of an exterior angle of a triangle is greater that the measurement of each of its remote interior angles

Front 17

Parallel Postulate

Back 17

Through a point not on a line, there is one and only one line parallel to the given line

Front 18

Spherical Geometry Parallel Postulate

Back 18

Through a point not on a line, there is no line parallel to the given line

Front 19

Polygon Angle-Sum Theorem

Back 19

The sum of the measures of the angles of an n-gon is (n-2)180

Front 20

Polygon Exterior Angle-Sum Theorem

Back 20

The sum of the measures of the exterior angles of a polygon, one at each vertex is 360

Front 21

Slopes of Parallel Lines

Back 21

If 2 nonvertical lines are parallel, their slopes are equal. If the slopes of 2 distinct nonvertical lines are equal the lines are parallel. Any 2 vertical lines are parallel

Front 22

Slopes of Perpedicular Lines

Back 22

If 2 nonvertical lines are perpendicular, the product of their slopes is -1. If the slopes of the 2 lines have a product of -1, the lines are perpendicular. Any horizontal line & vertical line are perpendicular

Front 23

Theorem 4-1

Back 23

If the 2 angles of one triangle are congruent to two angles of another triangle, then the 3rd angles are congruent

Front 24

Side-Side-Side (SSS) Postulate

Back 24

If the 3 sides of 1 triangle are congruent to the 3 sides of another triangle, then the 2 triangles are congruent

Front 25

Side-Angle-Side (SAS) Postulate

Back 25

If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent

Front 26

Angle-Side-Angle (ASA) Postulate

Back 26

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent

Front 27

Angle-Side-Angle (AAS) Theorem

Back 27

If 2 angles and a nonincluded side of one triangle are congruent to 2 angles and the corresponding nonincluded side of another triangle, then the triangles are congruent

Front 28

Isosceles Triangle Theorem

Back 28

If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent

Front 29

Converse of the Isosceles Triangle Theorem

Back 29

If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent

Front 30

Corollary

Back 30

If a triangle is equiangular, then the triangle is equilateral

Front 31

Theorem 4-5

Back 31

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base

Front 32

Hypotenuse-Leg (HL) Theorem

Back 32

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Front 33

Corollary

Back 33

If a triangle is equilateral, then the triangle is equilateral

Front 34

Corollary

Back 34

If a triangle is equilateral, then the triangle is equiangular