1. 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

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 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

14. 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.

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

16. What is a DIAGONAL?

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

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

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

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

21. 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.

22. Example 4 Using Theorem 6 – 4

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