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**Properties of Kites 6-6 and Trapezoids Warm Up Lesson Presentation**

Lesson Quiz Holt Geometry

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Do Now Solve for x. 1. x = 3x2 – 12 x = 180 3. 4. Find FE.

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Objectives TSW use properties of kites and trapezoids to solve problems.

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**Vocabulary kite trapezoid base of a trapezoid leg of a trapezoid**

base angle of a trapezoid isosceles trapezoid midsegment of a trapezoid

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**A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.**

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**Example 1: Problem-Solving Application**

Lucy is framing a kite with wooden dowels. She uses two dowels that measure 18 cm, one dowel that measures 30 cm, and two dowels that measure 27 cm. To complete the kite, she needs a dowel to place along . She has a dowel that is 36 cm long. About how much wood will she have left after cutting the last dowel?

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Example 2 What if...? Daryl is going to make a kite by doubling all the measures in the kite. What is the total amount of binding needed to cover the edges of his kite? How many packages of binding must Daryl buy?

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**Example 3: Using Properties of Kites**

In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.

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**Example 3.5: Using Properties of Kites**

In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mABC.

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**Example 4: Using Properties of Kites**

In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.

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Example 5 In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT.

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Example 5a In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQPS.

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Example 5b In kite PQRS, mPQR = 78°, and mTRS = 59°. Find each mPSR.

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**A trapezoid is a quadrilateral with exactly one pair of parallel sides**

A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.

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If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

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**Example 6: Using Properties of Isosceles Trapezoids**

Find mA.

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**Example 7: Using Properties of Isosceles Trapezoids**

KB = 21.9m and MF = Find FB.

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Example 8 Find mF.

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Example 9 JN = 10.6, and NL = Find KM.

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**Example 10: Applying Conditions for Isosceles Trapezoids**

Find the value of a so that PQRS is isosceles.

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**Example 11: Applying Conditions for Isosceles Trapezoids**

AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

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Example 12 Find the value of x so that PQST is isosceles.

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The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.

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**Example 13: Finding Lengths Using Midsegments**

Find EF.

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Example 14 Find EH.

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Lesson Quiz: Part I 1. Erin is making a kite based on the pattern below. About how much binding does Erin need to cover the edges of the kite? In kite HJKL, mKLP = 72°, and mHJP = 49.5°. Find each measure. 2. mLHJ 3. mPKL about in. 81° 18°

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Lesson Quiz: Part II Use the diagram for Items 4 and 5. 4. mWZY = 61°. Find mWXY. 5. XV = 4.6, and WY = Find VZ. 6. Find LP. 119° 9.6 18

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