1. Tests for Parallelograms
Theorem 8.9
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 8.10
If both pairs of opposite angles of a quadrilateral are equal, then the quadrilateral is a parallelogram.

2. Tests for Parallelograms
Theorem 8.11
If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
Theorem 8.12
If one pair of opposite sides of a quadrilateral is both equal and parallel, then the quadrilateral is a parallelogram.

3. Determine whether the quadrilateral is a parallelogram
Determine whether the quadrilateral is a parallelogram. Justify your answer.
Answer: One pair of opposite sides is parallel and has the same measure, which means these sides are congruent. If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.
Example 3-3b

4. Find m and n so that each quadrilateral is a parallelogram.b.
Answer:
Answer:
Example 3-4e

5. Determine whether the figure with the given vertices is a parallelogram. Use the method indicated.
a. A(–1, –2), B(–3, 1), C(1, 2), D(3, –1);
Slope Formula
Example 3-5f

6. Answer: The slopes of and the slopes of Therefore,
Answer: The slopes of and the slopes of Therefore, Since opposite sides are parallel, ABCD is a parallelogram.
Example 3-5f