Geometry Postulates/theorems Chapter 9

Front 1

9-1

Back 1

Two parallel lines lie in exactly one plane

Front 2

9-2

Back 2

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

Front 3

9-3

Back 3

Let L be a line and let P be a point not on L. Then there is at least one line through P, parallel to L

Front 4

9-4

Back 4

If two lines are cut by a transversal, and one pair of alternate interior angles are congruent, then the other pair of alternate interior angles are also congruent

Front 5

9-5

Back 5

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

Front 6

9-6

Back 6

Given two lines cut by a transversal. If a pair of corresponding angles are congruent, then a pair of alternate interior angles are congruent

Front 7

9-7

Back 7

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

Front 8

9-8

Back 8

Given two lines cut by a transversal. If a pair of interior angles on the same side of the transversal are supplementary, the lines are parallel

Front 9

9-9

Back 9

If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent

Front 10

9-10

Back 10

In a plane, if a line intersects one of two parallel lines in only one point, then it intersects the other

Front 11

9-11

Back 11

In a plane, if two lines are each parallel to a third line, then they are parallel to each other

Front 12

9-12

Back 12

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

Front 13

9-13

Back 13

For every triangle, the sum of the measures of the angles is 180

Front 14

9-14

Back 14

Each diagonal separates a parallelogram into two congruent triangles

Front 15

9-15

Back 15

In a parallelogram, any two opposite sides are congruent

Front 16

9-16

Back 16

In a parallelogram, any two opposite angles are congruent

Front 17

9-17

Back 17

In a parallelogram, any two consecutive angles are supplementary

Front 18

9-18

Back 18

The diagonals of a parallelogram bisect each other

Front 19

9-19

Back 19

Given a quadrilateral in which both pairs of oposite sides are congruent. Then the quadrilateral is a parallelogram

Front 20

9-20

Back 20

If two sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram

Front 21

9-21

Back 21

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Front 22

9-22

Back 22

The segment between the mid-points of two sides of a triangle is parallel to the third side and half as long

Front 23

9-23

Back 23

If a parallelogram has one right angle, then it has four right angles, and the parallelogram is a rectangle

Front 24

9-24

Back 24

In a rhombus, the diagonals are perpendicular to one another

Front 25

9-25

Back 25

If the diagonals of a quadrilateral bisect each other and are perpendicular, then the quadrilateral is a rhombus

Front 26

9-26

Back 26

The median to the hypotenuse of a right triangle is half as long as the hypotenuse

Front 27

9-27
30-60-90 Triangle Theorem

Back 27

If an acute angle of a right triangle has measure 30, then the opposite side is half as long as the hypotenuse

Front 28

9-28

Back 28

If one leg of a right triangle is half as long as the hypotenuse, then the opposite angle has measure 30

Front 29

9-29

Back 29

If three parallel lines intercept congruent segments on one transversal T, then they intercept congruent segments on every transversal T' which is parallel to T

Front 30

9-30

Back 30

If three parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any other transversal