Lesson 5.6. 1. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram (reverse of the definition).

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Presentation transcript:

Lesson 5.6

1. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram (reverse of the definition). 2. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property). 3. If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.

4. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram (converse of a property). 5. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property).

1.ACDF is a. 2.  A   D 3.AF  DC 4.  AFB   ECD 5.ΔAFB  ΔDCE 6.FB  EC 7.AB  ED 8.AC  FD 9.BC  FE 10.FBCE is a. 1.Given 2.Opposite  s of a are . 3.Opposite sides of a are . 4.Given 5.ASA (2,3,4) 6.CPCTC 7.CPCTC 8.Same as 3 9.Subtraction property. 10.If both pairs of opposite sides of a quadrilateral are , it is a.

In order for QUAD to be a parallelogram, opposite angles have to be congruent.  Q = 3x(x 2 – 5x) = 3x 3 – 15x 2  A = 3x 3 – 15x 2 Therefore,  Q &  A are congruent.  U = (x 2 ) 5 = x 10  D = x 10 Therefore,  U &  D are congruent. With opposite angles congruent, QUAD is a parallelogram.