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Proving that a Quadrilateral is a Parallelogram

Proving that a Quadrilateral is a Parallelogram. 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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Proving that a Quadrilateral is a Parallelogram

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  1. Proving that a Quadrilateral is a Parallelogram Lesson 5.6

  2. 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.

  3. 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).

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

  5. In order for QUAD to be a parallelogram, opposite angles have to be congruent. Q = 3x(x2 – 5x) = 3x3 – 15x2 A = 3x3 – 15x2 Therefore, Q & A are congruent. U = (x2)5 = x10 D = x10 Therefore, U & D are congruent. With opposite angles congruent, QUAD is a parallelogram.

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