Chapter 8 And 9 Theorems

Front 1

Theorem 8.1

Back 1

Polygon Interior Angles Theorem- The sum of the measures of the interior angles of a convex n-gon is (n-2)*180.

Front 2

Theorem 8.2

Back 2

Polygon Exterior Angles Theorem- The sum of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Front 3

Theorem 8.3

Back 3

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Front 4

Theorem 8.4

Back 4

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Front 5

Theorem 8.5

Back 5

If a quadrilateral is a parallelogram, then it's consecutive angles are supplementary.

Front 6

Theorem 8.6

Back 6

If a quadrilateral is a parallelogramm, then its diagonals bisect each other.

Front 7

Theorem 8.7

Back 7

If both pairs of opposites sides are congruent, then the quadrilateral is a parallelogram.

Front 8

Theorem 8.8

Back 8

If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

Front 9

Theorem 8.9

Back 9

If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.

Front 10

Theorem 8.10

Back 10

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

Front 11

Theorem 8.11

Back 11

A parallelogram is a rhombus if and only if its diagonals are perpendicular.

Front 12

Theorem 8.12

Back 12

A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

Front 13

Theorem 8.13

Back 13

A parallelogram is a rectangle if and only if its diagonals are congruent.

Front 14

Theorem 8.14

Back 14

If a trapezoid is isosceles, then both pairs of base angles are congruent.

Front 15

Theorem 8.15

Back 15

If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Front 16

Theorem 8.16

Back 16

A trapezoid is isosceles if and only if its diagonals are congruent.

Front 17

Theorem 8.17

Back 17

Midsegment Theorem for Trapezoids- The midsegment of a trapezoid is parallel to each base and its lengths is one half the sum of the length of the bases.

Front 18

Theorem 8.18

Back 18

If the quadrilateral is a kite, then its diagonals are perpendicular.

Front 19

Theorem 8.19

Back 19

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

Front 20

Theorem 9.1

Back 20

Translation Theorem- A translation is an isometry.

Front 21

Theorem 9.2

Back 21

Reflection Theorem- A reflection is an isometry.

Front 22

Theorem 9.3

Back 22

Rotation Theorem- A rotation is an isometry.

Front 23

Theorem 9.4

Back 23

Composition Theorem- The composition of two (or more) isometries is an isometry.

Front 24

Theorem 9.5

Back 24

Reflections in Parallel Lines- If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is the same as a translation. If P" is the image of P, then:
(1) segment PP is perpendicular to k and m, and
(2) PP" = 2d, where d is the distance between k and m.

Front 25

Theorem 9.6

Back 25

Reflections in Intersecting Lines- If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is the same as a rotation about point P. The angle of rotation is 2x (degrees), where x (degrees) is the measure of the acute or right angle formed by k and m.