## Geometry Chapter 8

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Selena53  on February 28, 2011

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# Geometry Chapter 8

 Polygon Interior Angles TheoremThe sum of the measures of the interior angles of a convex n-gon is (n-2) × 180°.
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#### Definitions

Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2) × 180°.
Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360°.
Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°.
Congruent Opposite Sides in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Congruent Opposite Angles in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Supplementary Consecutive Angles in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Bisecting Diagonals in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Congruent Opposite Sides in a Parallelogram Converse If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Congruent Opposite Angles in a Parallelogram Converse If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Congruent & Parallel Opposite Side Pair in a Parallelogram Theorem If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.
Bisecting Diagonals in a Parallelogram Converse If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Rhombus Corollary A quadrilateral is a rhombus if and only if it has four congruent sides.
Rectangle Corollary A quadrilateral is a rectangle if and only if it has four right angles.
Square Corollary A quadrilateral is a square if and only if it is a rhombus (4 congruent sides) and a rectangle (4 right angles).
Perpendicular Diagonals in a Rhombus Theorem A parallelogram is a rhombus if and only if it's diagonals are perpendicular.
Angle Bisecting Diagonals in a Rhombus Theorem A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
Congruent Diagonals in a Rectangle Theorem A parallelogram is a rectangle if and only if its diagonals are congruent.
Congruent Base Angle Pairs in an Isosceles Trapezoid Theorem If a trapezoid is isosceles, then each pair of base angles is congruent.
Congruent Base Angle Pairs in an Isosceles Trapezoid Converse If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
Congruent Diagonals in an Isosceles Trapezoid Theorem A trapezoid is isosceles if and only if its diagonals are congruent.
Midsegment Theorem for Trapezoids The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
Perpendicular Diagonals in a Kite Theorem If a quadrilateral is a kite, then its diagonals are perpendicular.
Congruent Opposite Angle Pair in a Kite Theorem If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
Parallel Sides
Opposite Congruent
1 Parallel and Congruent
Diagonals Bisect
Ways to Prove Quadrilateral is a Parallelogram (P.S. the OC is DiaBolical and it is on at five Pacific standard time on a Clock) (caps letters stand for ways to prove)

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