# POLYGONS AND QUADRILATERALS

### SHORE FLEURY

## GEOMETRIC KITE

## Theorem 6-22 If a quadrilateral is a kite, then its diagonals are perpendicular. | ## Real Life Example: #1 Proving this theorem correct. | ## Real Life Example: #2 Proving this theorem correct again. |

## KITE PROBLEM

## Problem #1 Explanation

Problem #1: Finding Angle Measures in Kites

Measure of angle 1=90 (Diagonals of a kite are perpendicular)

90+52+measure of angle 2=180 (Triangle-Sum Theorem)

142+measure of angle 2=180 (Simplify)

Measure of angle 2 =38 (Subtract 142 from each side)

Triangle ADC is congruent to triangle ABC by SSS. Since corresponding parts of congruent triangles are congruent, the measure of angle 3 equals the measure of angle BAC equals 52.

## TRAPEZOIDS AND ISOSCELES TRAPEZOIDS

## Trapezoid Definition: A quadrilateral with exactly one pair of parallel sides | ## Isosceles Trapezoid Definition: a trapezoid with legs that are congruent |

## Compare and Contrast

## TRAPEZOID PROBLEM

## PROBLEM #1 EXPLANATION

ABCD is an isosceles trapezoid and the measure of angle A= 65.

Measure of Angle A + Measure of Angle B= 180 (Two angles that form same-side interior angles along one leg are supplementary)

65+the measure of angle B=180 (Substitute)

The measure of angle B=115 (Subtract 65 from each side)

Since each pair of base angles of an isosceles trapezoid is congruent the measure of angle A & D are 65 degrees and the measures of angle B & C are 115 degrees.

## PARALLELOGRAMS

## RHOMBUS A parallelogram with four congruent sides. | ## RECTANGLE A parallelogram with four right angles. | ## SQUARE A parallelogram with four congruent sides and four right angles. |

## REAL LIFE EXAMPLES OF PARALLELOGRAMS

## REAL LIFE EXAMPLE #1 An eraser is a real life example of a parallelogram because it is considered to be a rhombus. A rhombus has four congruent sides. | ## REAL LIFE EXAMPLE #2 A dollar bill is a real life example of a parallelogram because it is considered to be a rectangle. A rectangle has four right angles. |

## REAL LIFE EXAMPLE #1

## PARALLELOGRAM PROBLEM

## PROBLEM #1 EXPLANATION

Finding the missing angles:

First: solve for one of the variables by setting the two equations given equal to each other.

In this case, first equation is setting (4x-21)=3x

Subtracting 21 from each side and subtracting 3x to get x=21

Use substitution to find the missing angles (Angle B & Angle D= 63 Degrees)

Second: Consecutive angles are equal to 180.

Therefore, I used Angle A and Angle B and set those equations equal to 180 (3y+63=180)

Subtract 63 from both sides to get 3y=117

Divide 3 to get y by itself. (y=39)

Use substitution to find the missing angles (Angle A & Angle C= 117 Degrees)

## PROPERTIES OF PARALLELOGRAMS

▪In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

## CONSECUTIVE ANGLES

## THEOREM 6-3

## THEOREM 6-4

## THEOREM 6-5

## THEOREM 6-6

## THEOREM 6-7

## Geometric Shapes Video

## SOURCES!

*Pearson EText Sign In Page*. N.p., n.d. Web. 29 Jan. 2016.

Used Notes taken in class!!!