1. In the figure, LMNO is a rhombus. Find x. Find y.
3. In the figure, QRST is a square.
Find n if mTQR = 8n + 8.
4. Find w if QR = 5w + 4 and RS = 2(4w –7).
5. Find QU if QS = 16t – 14 and QU = 6t + 11.
Lesson 6 Menu

2. Recognize and apply the properties of trapezoids.
Solve problems involving the medians of trapezoids.
trapezoid
isosceles trapezoid
median
Lesson 6 MI/Vocab

3. Lesson 6 TH1

4. Given: KLMN is an isosceles trapezoid.
Proof of Theorem 6.19
Write a flow proof.
Given: KLMN is an isosceles trapezoid.
Prove:
Lesson 6 Ex1

5. Proof of Theorem 6.19
Proof:
Lesson 6 Ex1

6. Given: ABCD is an isosceles trapezoid.
Write a flow proof.
Given: ABCD is an isosceles trapezoid.
Prove:
Lesson 6 CYP1

7. Which reason best completes the flow proof?
A. Substitution
B. Definition of trapezoid
C. CPCTC
D. Diagonals of an isosceles trapezoid are . A B C D
Lesson 6 CYP1

8. Identify Isosceles Trapezoids
The top of this work station appears to be two adjacent trapezoids. Determine if they are isosceles trapezoids.
Each pair of base angles is congruent, so the legs are the same length.
Answer: Both trapezoids are isosceles.
Lesson 6 Ex2

9. The sides of a picture frame appear to be two adjacent trapezoids
The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids.
A. yes
B. no
C. cannot be determined A. B. C.
Lesson 6 CYP2

10. Identify Trapezoids
A. ABCD is a quadrilateral with vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Verify that ABCD is a trapezoid.
A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula.
Lesson 6 Ex3

11. Identify Trapezoids slope of slope of slope of
Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid.
Lesson 6 Ex3

12. Identify Trapezoids
B. ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain.
Lesson 6 Ex3

13. Use the Distance Formula to show that the legs are congruent.
Identify Trapezoids
Use the Distance Formula to show that the legs are congruent.
Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid.
Lesson 6 Ex3

14. Lesson 6 TH2

15. Median of a Trapezoid
A. DEFG is an isosceles trapezoid with median Find DG if EF = 20 and MN = 30.
Lesson 6 Ex4

16. Subtract 20 from each side.
Median of a Trapezoid
Theorem 8.20
Substitution
Multiply each side by 2.
Subtract 20 from each side.
Answer: DG = 40
Lesson 6 Ex4

17. Because this is an isosceles trapezoid,
Median of a Trapezoid
B. DEFG is an isosceles trapezoid with median Find m1, m2, m3, and m4 if m1 = 3x + 5 and m3 = 6x – 5.
Because this is an isosceles trapezoid,
Lesson 6 Ex4

18. Consecutive Interior Angles Theorem
Median of a Trapezoid
Consecutive Interior Angles Theorem
Substitution
Combine like terms.
Divide each side by 9.
Answer: If x = 20, then m1 = 65 and m3 = 115. Because 1  2 and 3  4, m2 = 65 and m4 = 115.
Lesson 6 Ex4

19. A. WXYZ is an isosceles trapezoid with median Find XY if JK = 18 and WZ = 25.
A. XY = 32
B. XY = 25
C. XY = 21.5
D. XY = 11 A B C D
Lesson 6 CYP4

20. B. WXYZ is an isosceles trapezoid with median If m2 = 43, find m3.
A. m3 = 60
B. m3 = 34
C. m3 = 43
D. m3 = 137 A B C D
Lesson 6 CYP4