Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Theorem 5.18 If a quadrilateral is a parallelogram, then its opposite sides are congruent. P S R Q If PQRS is a parallelogram, then

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Theorem 5.19 If a quadrilateral is a parallelogram, then its opposite angles are congruent. P S R Q If PQRS is a parallelogram, then

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Example 1 Use properties of parallelograms F J H G Find the value of x and y. Solution FGHJ is a parallelogram by the definition of a parallelogram. Use Theorem 5.18 to find the value of x. Opposite sides of a are . Substitute x + 6 for FG and __ for ___. Subtract 6 from both sides. By Theorem 5.19, In FGHJ, x = ___ and y = _____.

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Theorem 5.20 If a quadrilateral is a parallelogram, then its consecutive angles are _______________. supplementary P S R Q If PQRS is a parallelogram, then

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Example 2 Use properties of a parallelogram Gates As shown, a gate contains several parallelograms. A D C B Solution By Theorem 5.20, the consecutive angle pairs in ABCD are ______________. supplementary

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Checkpoint. Find the indicated measure in LMN shown at the right. L K M N x By Theorem 5.18, opposite sides are congruent.

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Checkpoint. Find the indicated measure in LMN shown at the right. L K M N y By Theorem 5.19, opposite angles are congruent.

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Checkpoint. Find the indicated measure in LMN shown at the right. L K M N z By Theorem 5.20, consecutive angles are supplementary.

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Theorem 5.21 If a quadrilateral is a parallelogram, then its diagonals _________ each other. bisect P S R Q

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Example 3 Find the intersection of diagonals The diagonals of STUV intersect at point W. Find the coordinates of W. T S W V U Solution By Theorem 5.21, the diagonals of a parallelogram _______ each other. So, W is the _________ of the diagonals TV and SU. bisect midpoint Use the _____________________. Midpoint Formula Coordinates of the midpoint W of

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Checkpoint. Complete the following exercises. The diagonals of VWXY intersect at point Z. Find the coordinates of Z W V Z Y X By Theorem 5.21, the diagonals of a parallelogram bisect each other. So, Z is the midpoint of the diagonals WY and VX.

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Checkpoint. Complete the following exercises. Given that FGHJ is a parallelogram, find MH and FH. F M J H G By Theorem 5.21, the diagonals of a parallelogram bisect each other. So, M is the midpoint of the diagonal FH.

Use Properties of Parallelograms 5.8 Use Properties of Parallelograms Pg. 318, 5.8 #2-34 even