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6-3 Tests for Parallelograms

6-3 Tests for Parallelograms. You recognized and applied properties of parallelograms. Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove that a set of points forms a parallelogram in the coordinate plane. Properties of Parallelograms.

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6-3 Tests for Parallelograms

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  1. 6-3 Tests for Parallelograms You recognized and applied properties of parallelograms. • Recognize the conditions that ensure a quadrilateral is a parallelogram. • Prove that a set of points forms a parallelogram in the coordinate plane.

  2. Properties of Parallelograms • The opposite sides of a parallelogram are parallel (by definition). • The opposite angles of a parallelogram are congruent. • The opposite sides of a parallelogram are congruent. • The consecutive angles of a parallelogram are supplementary. • The diagonals of a parallelogram bisect each other.

  3. Write the Converse of the definition The opposite sides of a parallelogram are parallel (by definition). A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition). • Draw a parallelogram on a piece of graph paper. • How do you check for 2 pairs of parallel sides?

  4. Write the converse of: The opposite angles of a parallelogram are congruent. If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 1. Measure the angles of your parallelogram.

  5. Write the Converse of The opposite sides of a parallelogram are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 1. Measure the length of the sides of your quadrilateral. Write down the measurements.

  6. Write the Converse of The consecutive angles of a parallelogram are supplementary. If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. 1. Add up the measures of the consecutive angles. Are they supplementary?

  7. Write the Converse of The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. • Draw diagonals in your quadrilateral. • Measure the diagonals. • Measure each part of the diagonals and write down the measurement.

  8. Page 413

  9. 110° 70° 110° Is the quadrilateral a parallelogram? Yes, Opposite sides are congruent. Yes, diagonals bisect each other. ?? The congruent sides may not be parallel. Yes, consecutive angles are supplementary.

  10. Determine whether the quadrilateral is a parallelogram. Justify your answer. Answer: Each pair of opposite sides has the same measure. Therefore, they are congruent.If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

  11. Which method would prove the quadrilateral is a parallelogram? A. Both pairs of opp. sides ||. B. Both pairs of opp. sides . C. Both pairs of opp. s . D. One pair of opp. sides both || and .

  12. Find x and y so that the quadrilateral is a parallelogram. Opposite sides of a parallelogram are congruent. AB = DC Substitution Distributive Property Subtract 3x from each side. Add 1 to each side.

  13. Substitution Distributive Property Subtract 3y from each side. Add 2 to each side. Answer: So, when x = 7 and y = 5, quadrilateral ABCD is a parallelogram.

  14. Answer: Since opposite sides have the same slope, QR║ST and RS║TQ. Therefore, QRST is a parallelogram by definition. COORDINATE GEOMETRYQuadrilateral QRST has vertices Q(–1, 3), R(3, 1), S(2, –3), and T(–2, –1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula. If the opposite sides of a quadrilateral are parallel, then it is a parallelogram.

  15. Conditions for a Parallelogram • A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition). • If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. • If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

  16. 6-3 Assignment Page 418, 9-14, 18-24 18-24 Show your work! No work, No credit

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