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

PARALLELOGRAM - Definition A parallelogram is a quadrilateral with BOTH pairs of opposite sides parallel.

We use a small parallelogram like prior to the vertices when naming a parallelogram. Naming Parallelograms TEAM

Practice naming the following parallelograms. Naming Parallelograms

Practice naming the following parallelograms. Naming Parallelograms

Examples *Images courtesy of Microsoft

If a quadrilateral is a parallelogram then its opposite sides are congruent.

If a quadrilateral is a parallelogram then its opposite angles are congruent.

If a quadrilateral is a parallelogram then its consecutive angles are supplementary.

Consecutive supplementary angle sets. SET 1 SET 2 SET 3 SET 4

If a quadrilateral is a parallelogram then its diagonals bisect each other.

Example 1: ACES is a parallelogram. Find the unknown lengths. a. CEb. FEc. AE

Example 1: ACES is a parallelogram. Find the unknown lengths. a. CE = 6m b. FE = 7m c. AE = 14m

Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D

A B C D 105 o Example 2: In parallelogram ABCD, m<C = 105 o. Find each angle measure. a. m<Ab. m<D

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

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

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 o = 180 o o -105 o m<B = 75 o 105 o

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 o = 180 o o -105 o m<B = 75 o

WX Y Z (3x + 18) o (4x - 9) o Example 3: WXYZ is a parallelogram. Find the value of x.

3x + 18 = 4x – 9 Example 3: WXYZ is a parallelogram. Find the value of x. WX Y Z (3x + 18) o (4x - 9) o

3x + 18 = 4x – 9 -3x 18 = x – = x Example 3: WXYZ is a parallelogram. Find the value of x. WX Y Z (3x + 18) o (4x - 9) 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.

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.

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.

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.