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Holt Geometry 6-6 Properties of Kites and Trapezoids To learn the properties of kites and trapezoids to solve problems. Learning Objectives 7-5

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Page 1: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

To learn the properties of kites and trapezoids to solve problems.

Learning Objectives

7-5

Page 2: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

kite

trapezoid

base of a trapezoid

leg of a trapezoid

base angle of a trapezoid

isosceles trapezoid

midsegment of a trapezoid

Vocabulary

7-5

Page 3: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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

7-5

Page 4: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids7-5

Page 5: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 1: Using Properties of Kites

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

7-5

Page 6: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 2: Using Properties of Kites

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

7-5

Page 7: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 3: Using Properties of Kites

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

7-5

Page 8: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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

Example 4: Using Properties of Kites

7-5

Page 9: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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

Example 5: Using Properties of Kites

7-5

Page 10: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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

Example 6: Using Properties of Kites

7-5

Page 11: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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.

7-5

Page 12: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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

7-5

Page 13: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids7-5

Page 14: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 7: Using Properties of Isosceles Trapezoids

Find mA.

7-5

Page 15: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 8: Using Properties of Isosceles Trapezoids

KB = 21.9m and MF = 32.7. Find FB.

7-5

Page 16: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Find mF.

Example 9: Using Properties of Isosceles Trapezoids

7-5

Page 17: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

JN = 10.6, and NL = 14.8. Find KM.

Example 10: Using Properties of Isosceles

Trapezoids

7-5

Page 18: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 11: Applying Conditions for Isosceles

Trapezoids

Find the value of a so that PQRSis isosceles.

7-5

Page 19: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 12: Applying Conditions for Isosceles

Trapezoids

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

7-5

Page 20: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Find the value of x so that PQST is isosceles.

Example 13: Applying Conditions for Isosceles

Trapezoids

7-5

Page 21: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

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.

7-5

Page 22: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids7-5

Page 23: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Example 14: Finding Lengths Using Midsegments

Find EF.

7-5

Page 24: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids

Find EH.

Example 15: Finding Lengths Using Midsegments

7-5

Page 25: Learning Objectives · Learning Objectives 7-5. Holt Geometry 6-6 Properties of Kites and Trapezoids kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid

Holt Geometry

6-6 Properties of Kites and Trapezoids7-5

Practice Questions are in the workbook on Page 167:1,4,6,8,9,11,14

Practice Questions are in the workbook on Page 167:20,21,22,26,27,29

And