Section 6 – 2Properties of

Parallelograms

Objectives:To use relationships among sides and among

angles of parallelogramsTo use relationships involving diagonals of

parallelograms or transversals

Theorem 6 – 1

Opposite sides of a parallelogram are congruent

Consecutive Angles:

Angles of a polygon that share a side

Consecutive angles are supplementary!

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?

B) Use ▱KMOQ to find m ∠ 0.

C) If m ∠ BAD = y and m ∠ ADC = 4y – 70, find y.

Theorem 6 – 2

Opposite angles of a parallelogram are congruent

Example 2 Using Algebra

A) Find the values of x in ▱PQRS. Then find QR and PS.

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

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

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.

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

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

Warm UpSolve each system of linear equations.

1) 2x = y + 4 2) 2x = y + 3x + 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.

Section 6 – 2Continued…

Objectives:To use relationships involving diagonals of

parallelograms or transversals

What is a DIAGONAL?

Theorem 6 – 3

The diagonals of a parallelogram bisect each other.

Example 3 Using Algebra

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

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

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

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.

Example 4 Using Theorem 6 – 4

A)

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