Splash screen
Download
1 / 36

Splash Screen - PowerPoint PPT Presentation


  • 77 Views
  • Uploaded on

Splash Screen. Five-Minute Check (over Lesson 6–5) Then/Now New Vocabulary Theorems: Isosceles Trapezoids Proof: Part of Theorem 6.23 Example 1: Real-World Example: Use Properties of Isosceles Trapezoids Example 2: Isosceles Trapezoids and Coordinate Geometry

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Splash Screen' - lirit


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Lesson menu

Five-Minute Check (over Lesson 6–5)

Then/Now

New Vocabulary

Theorems: Isosceles Trapezoids

Proof: Part of Theorem 6.23

Example 1: Real-World Example: Use Properties of Isosceles Trapezoids

Example 2: Isosceles Trapezoids and Coordinate Geometry

Theorem 6.24: Trapezoid Midsegment Theorem

Example 3: Standardized Test Example

Theorems: Kites

Example 4: Use Properties of Kites

Lesson Menu


5 minute check 1

A

B

C

D

LMNO is a rhombus. Find x.

A. 5

B. 7

C. 10

D. 12

5-Minute Check 1


5 minute check 2

A

B

C

D

LMNO is a rhombus. Find y.

A. 6.75

B. 8.625

C. 10.5

D. 12

5-Minute Check 2


5 minute check 3

A

B

C

D

QRST is a square. Find n if mTQR = 8n + 8.

A. 10.25

B. 9

C. 8.375

D. 6.5

5-Minute Check 3


5 minute check 4

A

B

C

D

A. 6

B. 5

C. 4

D. 3.3

_

QRST is a square. Find w if QR = 5w + 4 and RS = 2(4w – 7).

5-Minute Check 4


5 minute check 5

A

B

C

D

QRST is a square. Find QU if QS = 16t – 14 and QU = 6t + 11.

A. 9

B. 10

C. 54

D. 65

5-Minute Check 5


5 minute check 6

A

B

C

D

A.

B.

C.JM║LM

D.

Which statement is true about the figure shown whether it is a square or a rhombus?

5-Minute Check 6


Then now

You used properties of special parallelograms. (Lesson 6–5)

  • Apply properties of trapezoids.

  • Apply properties of kites.

Then/Now


Vocabulary

  • trapezoid

  • bases

  • legs of a trapezoid

  • base angles

  • isosceles trapezoid

  • midsegment of a trapezoid

  • kite

Vocabulary




Example 1a

Use Properties of Isosceles Trapezoids

A. BASKET Each side of the basket shown is an isosceles trapezoid. If mJML= 130, KN = 6.7 feet, and LN = 3.6 feet, find mMJK.

Example 1A


Example 1a1

Use Properties of Isosceles Trapezoids

Since JKLM is a trapezoid, JK║LM.

mJML + mMJK = 180 Consecutive Interior Angles Theorem

mJML + 130 = 180 Substitution

mJML = 50 Subtract 130 from each side.

Answer:mJML = 50

Example 1A


Example 1b

Use Properties of Isosceles Trapezoids

B. BASKET Each side of the basket shown is an isosceles trapezoid. If mJML= 130, KN = 6.7 feet, and JL is 10.3 feet, find MN.

Example 1B


Example 1b1

Since JKLM is an isosceles trapezoid, diagonals JL and KM are congruent.

Use Properties of Isosceles Trapezoids

JL= KM Definition of congruent

JL = KN + MN Segment Addition

10.3= 6.7 + MN Substitution

3.6= MN Subtract 6.7 from each side.

Answer:MN = 3.6

Example 1B


Example 1a2

A

B

C

D

A. Each side of the basket shown is an isosceles trapezoid. If mFGH = 124, FI = 9.8 feet, and IG = 4.3 feet, find mEFG.

A. 124

B. 62

C. 56

D. 112

Example 1A


Example 1b2

A

B

C

D

B. Each side of the basket shown is an isosceles trapezoid. If mFGH = 124, FI = 9.8 feet, and EG = 14.1 feet, find IH.

A. 4.3 ft

B. 8.6 ft

C. 9.8 ft

D. 14.1 ft

Example 1B


Example 2

Isosceles Trapezoids and Coordinate Geometry

Quadrilateral ABCD has vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.

A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula.

Example 2


Example 21

slope of

slope of

slope of

Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid.

Isosceles Trapezoids and Coordinate Geometry

Example 2


Example 22

Isosceles Trapezoids and Coordinate Geometry

Use the Distance Formula to show that the legs are congruent.

Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid.

Example 2


Example 23

A

B

C

D

Determine whether QRST is a trapezoid and if so, determine whether it is an isosceles trapezoid.

A. trapezoid; not isosceles

B. trapezoid; isosceles

C. not a trapezoid

D. cannot be determined

Example 2



Example 3

In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x.

Example 3


Example 31

Read the Test Item

You are given the measure of the midsegment of a trapezoid and the measures of one of its bases. You are asked to find the measure of the other base.

Solve the Test Item

Trapezoid Midsegment Theorem

Substitution

Example 3


Example 32

Multiply each side by 2.

Subtract 20 from each side.

Answer:x = 40

Example 3


Example 33

A

B

C

D

WXYZ is an isosceles trapezoid with medianFind XY if JK = 18 and WZ = 25.

A.XY = 32

B.XY = 25

C.XY = 21.5

D.XY = 11

Example 3



Example 4a

Use Properties of Kites

A. If WXYZ is a kite, find mXYZ.

Example 4A


Example 4a1

Use Properties of Kites

Since a kite only has one pair of congruent angles, which are between the two non-congruent sides,WXY  WZY. So, WZY = 121.

mW + mX + mY + mZ = 360 Polygon Interior Angles Sum Theorem

73 + 121 + mY + 121 = 360 Substitution

mY = 45 Simplify.

Answer:mY= 45

Example 4A


Example 4b

Use Properties of Kites

B. If MNPQ is a kite, find NP.

Example 4B


Example 4b1

Use Properties of Kites

Since the diagonals of a kite are perpendicular, they divide MNPQ into four right triangles. Use the Pythagorean Theorem to find MN, the length of the hypotenuse of right ΔMNR.

NR2 + MR2 = MN2 Pythagorean Theorem

(6)2 + (8)2 = MN2 Substitution

36 + 64 = MN2 Simplify.

100 = MN2 Add.

10 = MN Take the square root of each side.

Example 4B


Example 4b2

Since MN  NP, MN = NP. By substitution, NP = 10.

Use Properties of Kites

Answer:NP= 10

Example 4B


Example 4a2

A

B

C

D

A. If BCDE is a kite, find mCDE.

A. 28°

B. 36°

C. 42°

D. 55°

Example 4A


Example 4b3

A

B

C

D

B. If JKLM is a kite, find KL.

A. 5

B. 6

C. 7

D. 8

Example 4B