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

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Presentation transcript:

(The Reverse of Lesson 5.5) I can prove the a quadrilateral is a parallelogram Day 1

 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 _________________________. congruent parallel congruent bisect each other

 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

 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

 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

 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.

 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

F AB E D C Given: ACDF is a Prove: FBCE is a