Proving a quadrilateral is a Parallelogram

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

Proving a quadrilateral is a Parallelogram

How do we know if a Quadrilateral is a Parallelogram?

How do we know if a Quadrilateral is a Parallelogram? If it has two sets of parallel sides, then it is a parallelogram. (Definition) There are 4 other sets of conditions that show a quadrilateral is a parallelogram by logical conclusion. The diagonals bisect each. The opposite sides are congruent The opposite angles are congruent One pair of sides is both congruent and parallel.

Prove that if a quadrilateral’s opposite sides are congruent,then it is a parallelogram. A D STATEMENTS REASONS C Given: AB = CD BC = DA Prove: ABCD is a parallelogram B

Prove that if a quadrilateral’s diagonals bisect each other,then it is a parallelogram. A D STATEMENTS REASONS C Given: AE = CE BE = DE Prove: ABCD is a parallelogram E B

Is there enough information to determine if the quadrilateral is a parallelogram? A D 1. AB = DC, AB ll DC Yes. C 2. BE = ED, AB = CD No. 3.<DAC=<BCA,<BAC=DCA E B

Homework P 307 (7-15,20-29,32-34)