Chapter 6 Lesson 2Chapter 6 Lesson 2Chapter 6 Lesson 2Chapter 6 Lesson 2Objective:Objective: To use relationships To use relationships

among diagonals, angles and sides of among diagonals, angles and sides of parallelograms.parallelograms.

Properties of ParallelogramsTheorem 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.

Example 1: Using Consecutive Angles

Find m   S in     RSTW .                

  R and   S are consecutive angles of a parallelogram. They are supplementary.

Example 2: Using Consecutive Angles

Find m   O in     KMOQ .                

K M

OQ35°

  Q and   O are consecutive angles of a parallelogram. They are supplementary.

180 OmQm18035 Om

145Om

Theorem 6-2

Opposite angles of a parallelogram are congruent.

Example 3: Using Algebra

Find the value of x in      PQRS. Then find QR and PS. 

Example 4: Using Algebra

Find the value of y in parallelogram EFGH.                                  

GmEm 37346 yy

333 y11y

Theorem 6-3

The diagonals of a parallelogram bisect each other.

Example 5: Using AlgebraSolve 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.

yx 1xy 273 Diagonals

bisect each other.

Step 2: Solve for a variable and Substitute xx 27)1(3

Step 3: Solve for variables

xx 2733 xx 243

4x

yx 1y14

y5

Example 6: Using Algebra

Find the values of a and b.

                          Step 1: Write equations.

2ba8210 ab

Diagonals bisect each other.

Step 2: Solve for a variable and Substitute 8)2(210 bb

Step 3: Solve for variables

84210 bb4210 bb

14b

2ba214a

16a

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

congruent segments on every transversal.                           

DFBD

Assignment

Pg. 297-300#1-

22(evens); 24-37; 39; 52