Tests for Parallelograms

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

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 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

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

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

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