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Lesson 6 Menu

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

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Lesson 6 Menu

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

  5. Proof of Theorem 6.19 Proof: Lesson 6 Ex1

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

  7. Proof: • A • B • C • D Which reason best completes the flow proof? A. Substitution B. Definition of trapezoid C. CPCTC D. Diagonals of an isosceles trapezoid are . 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. Determine if they are isosceles trapezoids. • A. • B. • C. A. yes B. no C. cannot be determined 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. slope of slope of slope of Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid. Identify Trapezoids 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. 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. A. DEFG is an isosceles trapezoid with medianFind DG if EF = 20 and MN = 30. Median of a Trapezoid Lesson 6 Ex4

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

  18. 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 = 65and m4 = 115. Lesson 6 Ex4

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

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

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