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6.3:Proving That a Quadrilateral is a Parallelogram. Objective: To determine whether a quadrilateral is a parallelogram. Before, we were told that a figure was a parallelogram. Now, we are going to prove that it is. . Theorem:
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6.3:Proving That a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram
Before, we were told that a figure was a parallelogram. Now, we are going to prove that it is. Theorem: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a . Example: Find the values of x and y for which MLPN must be a parallelogram. L P 2x 21 y+1 16 M N
Theorem If one pair of opposite sides of a quadrilateral is BOTH congruent and parallel, then the quadrilateral is a parallelogram. EXAMPLES: Is there enough information to determine that the quadrilateral is a parallelogram? Explain. a.) b.) x x
Theorem If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a . Is there enough information to prove the quadrilateral a parallelogram? 6 2 2 6
Find the values of x and y that would make the quadrilateral a parallelogram. 3y x+1 6 18
Theorem If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a . EXAMPLES: Is there enough info to prove the quadrilateral a parallelogram?Explain. a.) b.) 95° 80° 100° 80° 100° 80° 85° 95°
Find the values of x and y that would make the quadrilateral a parallelogram. 4y 3x 120 60
