## GEOMETRIC KITE

Definition: a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent

## 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.

## Compare and Contrast

A trapezoid is a quadrilateral with exactly one pair of parallel sides and an isosceles trapezoid is a trapezoid with legs that are congruent and bases that are parallel.

## PROBLEM #1 EXPLANATION

Problem #: Finding Angle Measures in Trapezoids

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

Definition: A quadrilateral with both pairs of opposite sides parallel

## 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

Parallelograms have special properties regarding their sides, angles, and diagonals.

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

## CONSECUTIVE ANGLES

Definition: Angles of a polygon that share a side

## THEOREM 6-3

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

## THEOREM 6-4

If a quadrilateral is parallelogram, then its consecutive angles are supplementary

## THEOREM 6-5

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

## THEOREM 6-6

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

## THEOREM 6-7

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

## Geometric Shapes Video

Geometry: Introduction to the Polygon (quadrilateral, pentagon, hexagon and more)