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5.6 Proving a Quadrilateral is a Parallelogram

I can prove the a quadrilateral is a parallelogram. Day 1. 5.6 Proving a Quadrilateral is a Parallelogram. (The Reverse of Lesson 5.5). Proving a Quadrilateral is a Parallelogram. The definition of a parallelogram is:

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5.6 Proving a Quadrilateral is a Parallelogram

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  1. I can prove the a quadrilateral is a parallelogram Day 1 5.6 Proving a Quadrilateral is a Parallelogram (The Reverse of Lesson 5.5)

  2. Proving a Quadrilateral is a Parallelogram • The definition of a parallelogram is: A quadrilateral in which BOTH pairs of the opposite sides are _____________. Complete the following theorems: • The opposite sides of a parallelogram are _________________________. • The opposite angles of a parallelogram are _________________________. • The diagonals of a parallelogram _________________________. parallel congruent congruent bisect each other

  3. Proving a Quadrilateral is a Parallelogram • What would be the reverse of, • If the quadrilateral is a parallelogram then the opposite sides are congruent? • If the BOTH pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Parallelogram

  4. Proving a Quadrilateral is a Parallelogram • What would be the reverse of, • If the quadrilateral is a parallelogram then the opposite angles are congruent? • If BOTH pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Parallelogram

  5. Proving a Quadrilateral is a Parallelogram • What would be the reverse of, • If the quadrilateral is a parallelogram then the diagonals bisect each other? • If the diagonals of a quadrilateral bisect each other, • then the quadrilateral is a parallelogram. Parallelogram

  6. Proving a Quadrilateral is a Parallelogram • Why do we not state the reverse of the definition? • Because the definition is just that. It is not an if-then statement. So we simply write an if-then statement that fits… • If the opposite sides of a quadrilateral are parallel then it is a parallelogram.

  7. Proving a Quadrilateral is a Parallelogram • There is one extra way to find a quadrilateral to be a parallelogram. • If ONE pair of opposite sides of a quadrilateral are parallel … AND congruent, then the quadrilateral is a parallelogram. Parallelogram

  8. Example Proof E F D A B C Given: ACDF is a Prove: FBCE is a

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