THEOREM 8.7
If both pairs of opposite __________ of a quadrilateral
are congruent, then the quadrilateral is a
___________________________.
If AB  _____ and BC  _______,
then ABCD is a parallelogram.
THEOREM 8.8
If both pairs of opposite _________ of a quadrilateral
are congruent, then the quadrilateral is a parallelogram.
If A  ________ and B  _______,
then ABCD is a parallelogram.
Example 1
Basketball In the diagram, AB and DC represent adjustable supports
of a basketball hoop. Explain why AD is always parallel to BC
THEOREM 8.9
If one pair of opposite sides of a quadrilateral are ___________________
and _____________________,
then the quadrilateral is a parallelogram.
If
BC____ AD and BC ____ AD , then ABCD is a parallelogram.
THEOREM 8.10
If the diagonals of a quadrilateral _______________ each other, then the quadrilateral is a parallelogram.
If
BD and AC ______________ each other, then ABCD is a parallelogram.
Example 2
Explain how you know that B  D
PRACTICE
Complete the following exercises.
1. In quadrilateral GHJK, mG = 55°, mH = 125°, and mJ = 55°. Find mK.
2. Can you show that the quadrilateral
is a parallelogram?
1.
3. For what value of x is quadrilateral PQRS a
parallelogram?
WAYS TO PROVE A QUADRILATERAL IS A PARALLELOGRAM
Show both pairs of opposite sides
2. Show both pairs of opposite sides are
are parallel. (Definition)
congruent. (Theorem 8.7)
3. Show both pairs of opposite angles
are congruent. (Theorem 8.8)
4. Show one pair of opposite sides are
congruent and parallel. (Theorem 8.9)
5. Show the diagonals bisect each other (Theorem 8.10)
Example 3: For what value of x is quadrilateral DFGH a parallelogram?
Example 4: Use coordinate geometry
Show that quadrilateral KLMN is a parallelogram.