Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Theorem 5.22 If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. sides A D C B then ABCD is a parallelogram.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Theorem 5.23 If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. angles A D C B then ABCD is a parallelogram.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Theorem 5.24 If one pair of opposite sides of a quadrilateral are __________ and ________, then the quadrilateral is a parallelogram. congruent parallel A D C B then ABCD is a parallelogram.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Theorem 5.25 If the diagonals of a quadrilateral ______ each other, then the quadrilateral is a parallelogram. bisect A D C B then ABCD is a parallelogram.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Example 1 Identify parallelograms Explain how you know that quadrilateral ABCD is a parallelogram. B A C D a. By the _____________________________ you know that Corollary to Theorem 5.16 congruent Because both pairs of opposite angles are ___________, then ABCD is a parallelogram by ______________. Theorem 5.23

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Example 1 Identify parallelograms Explain how you know that quadrilateral ABCD is a parallelogram. A D B C E b. EC In the diagram AE = ____ and BE = ____. ED So, the diagonals bisect each other, and ABCD is a parallelogram by ______________. Theorem 5.25

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Checkpoint. Complete the following exercises. In quadrilateral GHJK, What theorem can you use to show that GHJK is a parallelogram. J H K G Theorem 5.23 shows that GHJK is a parallelogram.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. P R Q S T Example 2 Use algebra with parallelograms For what value of x is quadrilateral PQRS a parallelogram? By Theorem 5.25, if the diagonals of PQRS ______ each other, then it is a parallelogram. You are given that bisect Set the segment lengths equal. Substitute for PT and for _____. Subtract ____ from both sides. Divide each side by ____ . Quadrilateral PQRS is a parallelogram when x = ___.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Checkpoint. Complete the following exercises. For what value of x is quadrilateral DFGH a parallelogram. D H F G

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Example 3 Use coordinate geometry Show that quadrilateral KLMN is a parallelogram? One way is to show that a pair of sides are congruent and parallel. Then apply ________________. Theorem 5.24 First use the Distance Formula to show that KL and MN are ____________. congruent

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Example 3 Use coordinate geometry Show that quadrilateral KLMN is a parallelogram? Then use the slope formula to show that KL ____ MN. parallel KL and MN have the same slope, so they are _________. KL and MN are congruent and parallel. So, KLMN is a parallelogram by __________________. Theorem 5.24

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Checkpoint. Complete the following exercises. Explain another method that can be used to show that quadrilateral KLMN in Example 3 is a parallelogram. Draw the diagonals and find the point of intersection. Show that the diagonals bisect each other using Distance Formula. Apply Theorem 5.25.

Show that a Quad. is a Parallel. 5.9 Show that a Quad. is a Parallel. Pg. 324, 5.9 #2-22 even