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Chapter 6 Lesson 3. Objective: To determine whether a quadrilateral is a parallelogram. Theorem 6-5 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 6-6
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Chapter 6 Lesson 3 Objective: To determine whether a quadrilateral is a parallelogram.
Theorem 6-5 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 6-6 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
Example 1: Finding Values for Parallelograms Find values of x and y for which MLPN must be a parallelogram.
Example 2: Finding Values for Parallelograms Find values of a and c for which PQRS must be a parallelogram.
Theorem 6-7 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6-8 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Example 3: Is the Quadrilateral a Parallelogram? Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Yes, both pairs of opposite angles are congruent. No, the figure could be a kite.
Example 4: Is the Quadrilateral a Parallelogram? Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Yes, a pair of opposite sides are parallel and congruent. No, the figure could be a trapezoid.
