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Section 6 – 2 Properties of Parallelograms

Section 6 – 2 Properties of Parallelograms. Objectives: To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms or transversals. Theorem 6 – 1. Opposite sides of a parallelogram are congruent. Consecutive Angles :.

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Section 6 – 2 Properties of Parallelograms

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  1. Section 6 – 2Properties of Parallelograms Objectives: To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms or transversals

  2. Theorem 6 – 1 Opposite sides of a parallelogram are congruent

  3. Consecutive Angles: Angles of a polygon that share a side Consecutive angles are supplementary!

  4. Example 1 Using Consecutive Angles A) Find m ∠ S in ▱RSTW. If consecutive angles of a quadrilateral are supplementary, must the quadrilateral be a parallelogram?

  5. Use ▱KMOQ to find m ∠ 0. • If m ∠ BAD = y and m ∠ ADC = 4y – 70, find y.

  6. Theorem 6 – 2 Opposite angles of a parallelogram are congruent

  7. Example 2 Using Algebra A) Find the values of x in ▱PQRS. Then find QR and PS.

  8. Find the value of y in ▱EFGH. Then find m ∠ E, m ∠ G, m ∠ F, and m∠ H.

  9. C) Find the value of d in ▱ABCD. Then find m ∠ A.

  10. Example 3 Parallelograms & Perimeter A) Find the lengths of all four sides of ▱ABCD. The perimeter is 48 inches. AB is 5 inches less than BC.

  11. B) Find the lengths of all four sides of ▱ABCD. The perimeter is 92 cm. AD is 7 cm more than twice AB.

  12. Homework:Textbook Page297 – 298; #2 – 16 even, 39 - 41

  13. Warm Up Solve each system of linear equations. 1) 2x = y + 4 2) 2x = y + 3 x + 2 = y 3x = 2y 3) Find the lengths of all four sides of ▱ABCD. The perimeter is 92 cm. AD is 7 cm more than twice AB.

  14. Section 6 – 2Continued… Objectives: To use relationships involving diagonals of parallelograms or transversals

  15. What is a DIAGONAL?

  16. Theorem 6 – 3 The diagonals of a parallelogram bisect each other.

  17. Example 3 Using Algebra A) Find the values of x and y in ▱ABCD. Then find AE, EC, BE, and ED.

  18. B) Find the values of a and b. Then find WY and XZ.

  19. C) Find the values of x and y in ▱PQRS when PT = 2x – 7, TR = 3y – 9, QT = y – 1, and TS = 2y – 5.

  20. Theorem 6 – 4 If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  21. Example 4 Using Theorem 6 – 4 A)

  22. Homework:Textbook Page 298 – 300; # 17 – 22, 24 – 32 Even, 44 – 52 Even

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