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.

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.

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.

Find m and n so that each quadrilateral is a parallelogram.

Answer: Answer:

a. b.

Determine whether the figure with the given vertices is a parallelogram. Use the method indicated.

Slope Formulaa. A(–1, –2), B(–3, 1), C(1, 2), D(3, –1);

Answer: The slopes of and the

slopes of Therefore,

Since opposite sides are parallel, ABCD is a

parallelogram.