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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

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Splash screen

Splash Screen


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


Concept 1

Concept 1


Concept 2

Concept 2


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=180Consecutive InteriorAngles Theorem

mJML + 130=180Substitution

mJML=50Subtract 130 from eachside.

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=KMDefinition of congruent

JL=KN + MNSegment Addition

10.3=6.7 + MNSubstitution

3.6=MNSubtract 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


Concept 3

Concept 3


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 MidsegmentTheorem

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


Concept 4

Concept 4


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=360PolygonInterior AnglesSum Theorem

73 + 121 + mY + 121=360Substitution

mY=45Simplify.

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=MN2Pythagorean Theorem

(6)2 + (8)2=MN2Substitution

36 + 64=MN2Simplify.

100=MN2Add.

10=MNTake the square root ofeach 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


End of the lesson

End of the Lesson


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