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5.8

5.8. Use Properties of Parallelograms. Q. R. P. S. Theorem 5.18. If a quadrilateral is a parallelogram, then its opposite sides are congruent. If PQRS is a parallelogram, then. 5.8. Use Properties of Parallelograms. Q. R. P. S. Theorem 5.19.

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5.8

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  1. 5.8 Use Properties of Parallelograms Q R P S Theorem 5.18 If a quadrilateral is a parallelogram, then its opposite sides are congruent. If PQRS is a parallelogram, then

  2. 5.8 Use Properties of Parallelograms Q R P S Theorem 5.19 If a quadrilateral is a parallelogram, then its opposite angles are congruent. If PQRS is a parallelogram, then

  3. 5.8 Use Properties of Parallelograms G F H J Opposite sides of a are . By Theorem 5.19, In FGHJ, x = ___ and y = _____. Use properties of parallelograms Example 1 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. Substitute x + 6 for FG and __ for ___. Subtract 6 from both sides.

  4. 5.8 Use Properties of Parallelograms Q R P S Theorem 5.20 If a quadrilateral is a parallelogram, then its consecutive angles are _______________. supplementary If PQRS is a parallelogram, then

  5. 5.8 Use Properties of Parallelograms A B D C By Theorem 5.20, the consecutive angle pairs in ABCD are ______________. Use properties of a parallelogram Example 2 Gates As shown, a gate contains several parallelograms. Solution supplementary

  6. 5.8 Use Properties of Parallelograms Checkpoint. Find the indicated measure in LMN shown at the right. L M N K • x By Theorem 5.18, opposite sides are congruent.

  7. 5.8 Use Properties of Parallelograms Checkpoint. Find the indicated measure in LMN shown at the right. L M N K • y By Theorem 5.19, opposite angles are congruent.

  8. 5.8 Use Properties of Parallelograms Checkpoint. Find the indicated measure in LMN shown at the right. L M N K • z By Theorem 5.20, consecutive angles are supplementary.

  9. 5.8 Use Properties of Parallelograms Q R P S Theorem 5.21 If a quadrilateral is a parallelogram, then its diagonals _________ each other. bisect

  10. 5.8 Use Properties of Parallelograms U T W V S By Theorem 5.21, the diagonals of a parallelogram _______ each other. So, W is the _________ of the diagonals TV and SU. The diagonals of STUV intersect at point W. Find the coordinates of W. Find the intersection of diagonals Example 3 Solution bisect midpoint Midpoint Formula Use the _____________________. Coordinates of the midpoint W of

  11. 5.8 Use Properties of Parallelograms • The diagonals of VWXY intersect at point Z. Find the coordinates of Z X W Z V Y By Theorem 5.21, the diagonals of a parallelogram bisect each other. So, Z is the midpoint of the diagonals WY and VX. Checkpoint. Complete the following exercises.

  12. 5.8 Use Properties of Parallelograms • Given that FGHJ is a parallelogram, find MH and FH. G F M H J By Theorem 5.21, the diagonals of a parallelogram bisect each other. So, M is the midpoint of the diagonal FH. Checkpoint. Complete the following exercises.

  13. 5.8 Use Properties of Parallelograms Pg. 318, 5.8 #2-34 even

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