Parallelograms

Unit 8.2

What is a parallelogram

• Definition: a parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Properties of a Parallelogram

1. Opposite sides of a parallelogram are congruent

2. Opposite angles in a parallelogram are congruent

3. Consecutive angles in a parallelogram are supplementary

4. If a parallelogram has one right angle, it has four right angles

Page 413 Example 2

Problems 7 – 12 Page 414

• 7. 100

• 8. 80

• 9. 80

• 10. 30

• 11. 3a = 21; a = 7

• 12 2b + 3 = 45; b = 21

Properties of diagonals

• 1. diagonals of a parallelogram bisect each other

• 2. each diagonal of a parallelogram separates the parallelogram into two congruent triangles

Unit 8.2 Problems

Page 414-5

Problems 7 – 12, 16 – 31, 35, 36

Tests for Parallelograms

Unit 8.3

Four Tests

1. If both pairs of opposite sides of a quadrilateral are congruent

2. If both pairs of opposite angles of a quadrilateral are congruent

3. If the diagonals of a quadrilateral bisect each other

4. If one pair of opposite sides of a quadrilateral is both parallel and congruent (new)

Problems

• Problems 4 – 7 page 4214. No – one pair of opposite sides are not parallel

and congruent5. Yes: Opposite angles are congruent6. 5y = 2y + 12 3x – 18 = 2x - 5 3y = 12 → y = 4 x = 137. 3x – 17 = 2x + 24 5y – 6 = y + 58 x = 41 4y = 64

y = 16

Homework Unit 8.3

• Page 421-2 Problems 4 – 7, 13 – 18,

19 – 24, 37