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Lesson 8.2

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Definition: A 4-sided shape with parallel opposite sides

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

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Pg. 415 – 416: #(16 – 31) all

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

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 22) Alternate interior with

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 23) Alternate interior angles

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 24) Alternate interior angles

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 25) Consecutive angles of parallelogram are supplementary

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 26) Linear pair angles

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 27) Vertical angles

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 28) Opposite sides of parallelogram are congruent

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 29) Opposite sides of parallelogram are congruent

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 30) Diagonals of parallelogram bisect each other

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Practice and apply: Use MNPR to find each measure or value MN RP Q z – 3 4w – x – 4 83 o 38 o 33 o 2y + 5 Q # 22 – 31 31) Diagonals of parallelogram bisect each other

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