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Parallelograms Unit 8.2

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

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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

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Page 413 Example 2

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Problems 7 – 12 Page 414 7. 100 8. 80 9. 80 10. 30 11. 3a = 21; a = 7 12 2b + 3 = 45; b = 21

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Properties of diagonals 1. diagonals of a parallelogram bisect each other 2. each diagonal of a parallelogram separates the parallelogram into two congruent triangles

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Unit 8.2 Problems Page 414-5 Problems 7 – 12, 16 – 31, 35, 36

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Tests for Parallelograms Unit 8.3

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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)

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Problems Problems 4 – 7 page 421 4. No – one pair of opposite sides are not parallel and congruent 5. Yes: Opposite angles are congruent 6. 5y = 2y + 123x – 18 = 2x - 5 3y = 12 → y = 4 x = 13 7. 3x – 17 = 2x + 245y – 6 = y + 58 x = 414y = 64 y = 16

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Homework Unit 8.3 Page 421-2 Problems 4 – 7, 13 – 18, 19 – 24, 37

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