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Lesson 8.2

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**Definition: A 4-sided shape with parallel opposite sides**

Parallelogram Definition: A 4-sided shape with parallel opposite sides

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**Properties of parallelograms**

b Consecutive angles are supplementary Opposite sides are congruent Opposite angles are congruent a + b = 180o b a Properties of parallelograms Each Diagonal separates the parallelogram into two congruent triangles Diagonals bisect each other

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Assignment Pg. 415 – 416: #(16 – 31) all

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**Complete each statement about ABCD, Justify your answer**

Practice and apply: Q # 16 – 21 Complete each statement about ABCD, Justify your answer A B C D G Opposite angles of parallelogram are congruent Alternate interior angles Diagonals of parallelogram bisect each other Opposite sides of parallelogram are // Diagonal AD separates the Parallelogram into two congruent triangles Opposite angles of parallelogram are congruent 5

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 22) Alternate interior with 6

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 23) Alternate interior angles 7

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 24) Alternate interior angles 8

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 25) Consecutive angles of parallelogram are supplementary 9

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 26) Linear pair angles 10

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 27) Vertical angles 11

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 28) Opposite sides of parallelogram are congruent 12

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 29) Opposite sides of parallelogram are congruent 13

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 30) Diagonals of parallelogram bisect each other 14

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**Use MNPR to find each measure or value**

Practice and apply: Q # 22 – 31 M N R P Q 20 17.9 15.4 3z – 3 4w – 3 11.1 3x – 4 83o 38o 33o 2y + 5 Use MNPR to find each measure or value 31) Diagonals of parallelogram bisect each other 15

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Warm Up: Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving? What is the measure of CD?

Warm Up: Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving? What is the measure of CD?

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