Chapter 6 Lesson 2

1. Chapter 6 Lesson 2 Objective: To use relationships among diagonals, angles and sides of parallelograms.

2. Properties of Parallelograms Theorem 6-1 Opposite sides of a parallelogram are congruent. Angles of a polygon that share a side are consecutive angles. A parallelogram has opposite sides parallel. Its consecutive angles are same-side interior angles so they are supplementary. In    ABCD, consecutive angles B and C are supplementary, as are consecutive angles C and D.

3. Example 1: Using Consecutive Angles Find mS in     RSTW .                 R and   S are consecutive angles of a parallelogram. They are supplementary.

4. Example 2: Using Consecutive Angles Find mO in     KMOQ .                   Q and   O are consecutive angles of a parallelogram. They are supplementary. K M 35° Q O

5. Theorem 6-2 Opposite angles of a parallelogram are congruent.

6. Example 3: Using Algebra Find the value of x in      PQRS. Then find QR and PS. 

7. Example 4: Using Algebra Find the value of y in parallelogram EFGH.

8. Theorem 6-3 The diagonals of a parallelogram bisect each other.

9. Example 5: Using Algebra Solve a system of linear equations to find the values of x and y in       ABCD. Then find AE, EC, BE, and ED. Step 1: Write equations. Diagonals bisect each other. Step 2:Solve for a variable and Substitute Step 3: Solve for variables

10. Example 6: Using Algebra Find the values of a and b. Step 1: Write equations. Diagonals bisect each other. Step 2:Solve for a variable and Substitute Step 3: Solve for variables

11. 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.

12. Assignment