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Section 5-2 Proving a Quadrilateral is a Parallelogram

Learn the 5 ways to prove a quadrilateral is a parallelogram based on side and angle properties, and practice identifying parallelograms through markings and justifications.

michellejenkins
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Section 5-2 Proving a Quadrilateral is a Parallelogram

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  1. Section 5-2 Proving a Quadrilateral is a Parallelogram

  2. 1. If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram. (Definition of a Parallelogram). 2. If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram. 3. If one pair of opposite sides of a quadrilateral are both congruent and parallel, then it is a parallelogram. 4. If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram. 5. If the diagonals of a quadrilateral bisect one another, then it is a parallelogram. There are 5 ways to prove that a quadrilateral is a parallelogram. They are…

  3. You will be asked to list these 5 ways of proving a quadrilateral is a parallelogram on your next test.

  4. Check for Understanding – Examine the markings on each quadrilateral. Determine whether there is enough information to prove that the quadrilateral is a parallelogram. If there is, write the justification. 12 9 8 8 12 9 Yes. If one pair of opposite sides of a quadrilateral are both congruent and parallel, then it is a parallelogram. Yes. If both pairs of opposite sides in a quadrilateral are congruent, then it is a parallelogram.

  5. Check for Understanding – Examine the markings on each quadrilateral. Determine whether there is enough information to prove that the quadrilateral is a parallelogram. If there is, write the justification. 70 70 Yes. If the diagonals of a quadrilateral bisect one another, then it is a parallelogram. No! We need BOTH pairs of opposite angles to be congruent.

  6. Check for Understanding – Examine the markings on each quadrilateral. Determine whether there is enough information to prove that the quadrilateral is a parallelogram. If there is, write the justification. 70 70 110 Yes. If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram. Yes. Definition of a parallelogram.

  7. Check for Understanding – Examine the markings on each quadrilateral. Determine whether there is enough information to prove that the quadrilateral is a parallelogram. If there is, write the justification. No! To use the reason “If one pair of sides of a quadrilateral is both parallel and congruent, it has to be the SAME PAIR! No!

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