POLYGONS AND QUADRILATERALS

SHORE FLEURY

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GEOMETRIC KITE

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

KITE PROBLEM

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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

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.

TRAPEZOID PROBLEM

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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

REAL LIFE EXAMPLES OF PARALLELOGRAMS

PARALLELOGRAM PROBLEM

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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.

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CONSECUTIVE ANGLES

Definition: Angles of a polygon that share a side
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THEOREM 6-3

If a quadrilateral is a parallelogram, then its opposite sides are congruent.
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THEOREM 6-4

If a quadrilateral is parallelogram, then its consecutive angles are supplementary
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THEOREM 6-5

If a quadrilateral is a parallelogram, then its opposite angles are congruent.
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THEOREM 6-6

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

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

SOURCES!

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

Used Notes taken in class!!!