Thursday, September 21, 2023

# Geometry Trapezoid And Kite Worksheet Key

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Geometry – Section 5.6 Kites and Trapezoids

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Find the measures of the numbered angles in each kite. Use sliders a and b to change the side lengths of the kite.

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## Properties Of Trapezoids And Kites

Geometry 10.2 Areas of Trapezoids, Rhombuses and Kites

Now that weve seen several types of parallelograms, lets learn about figures that do not have the properties of parallelograms. Recall that parallelograms were quadrilaterals whose opposite sides were parallel. In this section, we will look at quadrilaterals whose opposite sides may intersect at some point. The two types of quadrilaterals we will study are called trapezoids and kites. Lets begin our study by learning some properties of trapezoids.

Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Since a trapezoid must have exactly one pair of parallel sides, we will need to prove that one pair of opposite sides is parallel and that the other is not in our two-column geometric proofs. If we forget to prove that one pair of opposite sides is not parallel, we do not eliminate the possibility that the quadrilateral is a parallelogram. Therefore, that step will be absolutely necessary when we work on different exercises involving trapezoids.

Before we dive right into our study of trapezoids, it will be necessary to learn the names of different parts of these quadrilaterals in order to be specific about its sides and angles. All trapezoids have two main parts: bases and legs. The opposite sides of a trapezoid that are parallel to each other are called bases. The remaining sides of the trapezoid, which intersect at some point if extended, are called the legs of the trapezoid.

Consider trapezoid ABCD shown below.

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## Trapezoid And Kite Worksheet

Name ________________________________________ < strong> Trapezoid< /strong> < strong> and< /strong> < strong> Kite< /strong> Homework Period ________________ Date ____________ 1. Name the figure < strong> and< /strong> find the measure of angles. name _________________________ m F = _______ m G = ______ m H = ________ 2. Name the figure < strong> and< /strong> find the measure of angles. name _________________________ m K = _______ m J = ________ 3. Given rectangle PQRS, find the measure of the angles. m PST = _______ m PTS = _______ m QPR = _______ m PTQ = _______ m SRT = _______ m PQR = _______ What type of triangle is PST ? ____________ PSR ? ____________ 4. Given square EFGH, find the measure of the angles. m EJF = _______ m HEG = _______ m EHG = _______ m FEG = _______ m FJG = _______ m FGE = _______ What type of triangle is EHG ? ____________ EJH ? ____________ 5. Given rhombus PQRS, find the measure of the angles. m PTS = _______ m PST = _______ m RST = _______ m QRS = _______ m QRP = _______ m RTS = _______ What type of triangle is PTS ? ____________ PQS ? ____________

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## Trapezoids And Kites Worksheet

Trapezoid PQRS given below is an isosceles trapezoid.

Find mP, mQ and mR.

Problem 2 :

Prove that the figure ABCD given below is a trapezoid.

Problem 3 :

A baker is making a cake like the one which is given below. The top layer of the cake has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer of the cake be?

Problem 4 :

In the kite WXYZ shown below, find the length of each side.

Problem 5 :

Find mG and mJ in the diagram shown below.

Given : PQRS is an isosceles trapezoid.

According to theorem on trapezoids, each pair of base angles in an isosceles trapezoid must be congruent.

So, we have

mS = mR = 50°

Because S and P are consecutive interior angles formed by parallel lines, they are supplementary.

So, we have

mS + mP = 180°

Substitute mS = 50°.

Subtract 50° from both sides.

mP = 130°

According to theorem on trapezoids, each pair of base angles in an isosceles trapezoid must be congruent.

So, we have

mR = 50°

Find the slope of each side of the figure ABCD above and compare the slopes of opposite sides.

We can find the slope using slope formula given below.

Slope of the line joining two points and :

Slope of AB = / = 5/ = -1

Slope of CD = / = -3/3 = -1

Because the slopes of AB and CD are equal, we have

AB || CD

Slope of BC = / = 2/4 = 1/2

Slope of AD = / = 4/2 = 2

The slopes of BC and AD are not equal. So BC and AD are not parallel.

Because AB CD and BC AD, ABCD is a trapezoid.