Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt...
-
Upload
devin-wilson -
Category
Documents
-
view
333 -
download
11
Transcript of Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt...
![Page 1: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/1.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids6-6 Properties of Kites and Trapezoids
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
![Page 2: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/2.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Do NowSolve for x.
1. x2 + 38 = 3x2 – 12
2. 137 + x = 180
3.
4. Find FE.
![Page 3: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/3.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
TSW use properties of kites and trapezoids to solve problems.
Objectives
![Page 4: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/4.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
kitetrapezoidbase of a trapezoidleg of a trapezoidbase angle of a trapezoidisosceles trapezoidmidsegment of a trapezoid
Vocabulary
![Page 5: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/5.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.
![Page 6: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/6.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
![Page 7: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/7.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
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?
![Page 8: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/8.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
![Page 9: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/9.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
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?
![Page 10: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/10.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
![Page 11: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/11.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.
![Page 12: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/12.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3.5: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mABC.
![Page 13: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/13.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 4: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.
![Page 14: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/14.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT.
![Page 15: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/15.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5a
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQPS.
![Page 16: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/16.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5b
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find each mPSR.
![Page 17: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/17.jpg)
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.
![Page 18: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/18.jpg)
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.
![Page 19: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/19.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
![Page 20: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/20.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 6: Using Properties of Isosceles Trapezoids
Find mA.
![Page 21: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/21.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 7: Using Properties of Isosceles Trapezoids
KB = 21.9m and MF = 32.7. Find FB.
![Page 22: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/22.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 8
Find mF.
![Page 23: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/23.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 9
JN = 10.6, and NL = 14.8. Find KM.
![Page 24: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/24.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 10: Applying Conditions for Isosceles Trapezoids
Find the value of a so that PQRS is isosceles.
![Page 25: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/25.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 11: Applying Conditions for Isosceles Trapezoids
AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.
![Page 26: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/26.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 12
Find the value of x so that PQST is isosceles.
![Page 27: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/27.jpg)
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.
![Page 28: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/28.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
![Page 29: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/29.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 13: Finding Lengths Using Midsegments
Find EF.
![Page 30: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/30.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 14
Find EH.
![Page 31: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/31.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
![Page 32: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/32.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
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 eachmeasure.
2. mLHJ 3. mPKL
about 191.2 in.
81° 18°
![Page 33: Holt Geometry 6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites and Trapezoids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.](https://reader031.fdocuments.us/reader031/viewer/2022012305/55144533550346414e8b4b6e/html5/thumbnails/33.jpg)
Holt Geometry
6-6 Properties of Kites and Trapezoids
Lesson Quiz: Part II
Use the diagram for Items 4 and 5.
4. mWZY = 61°. Find mWXY.
5. XV = 4.6, and WY = 14.2. Find VZ.
6. Find LP.
119°
9.6
18