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PARALLELOGRAMS In this lesson you will explore: The definition of a parallelogram. Special characteristics of parallelograms. How to apply the characteristics of parallelograms to solve problems. Common Core Standards: N-Q.1, N-Q.2, N-Q.3, G-CO.11, G-GPE.4, G-GPE.5
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PARALLELOGRAM - Definition A parallelogram is a quadrilateral with BOTH pairs of opposite sides parallel.
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We use a small parallelogram like prior to the vertices when naming a parallelogram. Naming Parallelograms TEAM
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Practice naming the following parallelograms. Naming Parallelograms
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Practice naming the following parallelograms. Naming Parallelograms
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Examples *Images courtesy of Microsoft
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If a quadrilateral is a parallelogram then its opposite sides are congruent.
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If a quadrilateral is a parallelogram then its opposite angles are congruent.
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If a quadrilateral is a parallelogram then its consecutive angles are supplementary.
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Consecutive supplementary angle sets. SET 1 SET 2 SET 3 SET 4
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If a quadrilateral is a parallelogram then its diagonals bisect each other.
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Example 1: ACES is a parallelogram. Find the unknown lengths. a. CEb. FEc. AE
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Example 1: ACES is a parallelogram. Find the unknown lengths. a. CE = 6m b. FE = 7m c. AE = 14m
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Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D
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A B C D 105 o Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D
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A B C D 105 o Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D 105 o
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A B C D Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D m<B + m<C = 180 o 105 o
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A B C D 75 o Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D m<B + m<C = 180 o m<B + 105 o = 180 o - 105 o -105 o m<B = 75 o 105 o
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Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<A = 105 o b. m<D = 75 o A B C D 105 o 75 o m<B + m<C = 180 o m<B + 105 o = 180 o - 105 o -105 o m<B = 75 o
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WX Y Z (3x + 18) o (4x - 9) o Example 3: WXYZ is a parallelogram. Find the value of x.
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3x + 18 = 4x – 9 Example 3: WXYZ is a parallelogram. Find the value of x. WX Y Z (3x + 18) o (4x - 9) o
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3x + 18 = 4x – 9 -3x 18 = x – 9 +9 +9 27 = x Example 3: WXYZ is a parallelogram. Find the value of x. WX Y Z (3x + 18) o (4x - 9) o
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Example 4: A four sided concrete slab has consecutive angle measures of 85 o, 94 o, 85 o, and 96 o. Is the slab a parallelogram? Explain.
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85 o 94 o 96 o Example 4: A four sided concrete slab has consecutive angle measures of 85 o, 94 o, 85 o, and 96 o. Is the slab a parallelogram? Explain.
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No. If the quadrilateral was a parallelogram, both pairs of opposite angles would be congruent. 85 o 94 o 96 o Example 4: A four sided concrete slab has consecutive angle measures of 85 o, 94 o, 85 o, and 96 o. Is the slab a parallelogram? Explain.
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PARALLELOGRAMS In this lesson you learned: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Parallelograms have special characteristics like: Both pairs of opposite angles are congruent. Both pairs of opposite sides are congruent. Consecutive angles are supplementary. The diagonals bisect each other. How to apply the characteristics of parallelograms to solve problems.
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