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Conditions for Parallelograms

Conditions for Parallelograms. Students will be able to show that a given quadrilateral is a parallelogram. Characteristics or Conditions. In the last section we learned five characteristics of a parallelogram. We use these when we already know the figure is a parallelogram.

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Conditions for Parallelograms

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  1. Conditions for Parallelograms Students will be able to show that a given quadrilateral is a parallelogram

  2. Characteristics or Conditions • In the last section we learned five characteristics of a parallelogram. We use these when we already know the figure is a parallelogram. • In this section, we will learn what conditions will prove that a quadrilateral is a parallelogram. If we have one of these, then we know we have a parallelogram. Unit G

  3. Condition 1: The Definition of a Parallelogram • If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram. A B D C Unit G

  4. Condition 2: One Pair of Opposite Sides • If one pair of opposite sides is both parallel and congruent, then the quadrilateral is a parallelogram. A B D C Unit G

  5. Condition 3: Both Pairs of Opposite Sides • If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram. A B D C Unit G

  6. Condition 4: Both Pairs of Opposite Angles • If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram. A B D C Unit G

  7. Condition 5: Consecutive Angles • If an angle is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. A B (180 – x)º (180 – x)º xº D C Unit G

  8. Condition 6: Bisecting Diagonals • If the diagonals bisect each other, then the quadrilateral is a parallelogram. A B D C Unit G

  9. Example 1: Determine if each quadrilateral is a parallelogram Yes.The 73° angle is supplementary to both its consecutive angles. No.Only one pair of opposite angles are congruent. The conditions for a parallelogram are not met. Unit G

  10. Example 2: Determine if each quadrilateral is a parallelogram Yes.Since angles 1 and 2 are congruent by the 3rd Angle Theorem, both pairs of opposite angles of the quadrilateral are congruent. 1 2 No.Two pairs of consecutive sides are congruent. None of the sets of conditions for a parallel-ogram are met. Unit G

  11. Example 3: • Find the values of a and b that would make the quadrilateral a parallelogram. 15a – 11 = 10a + 4 5a = 15 a = 3 5b + 6 = 8b – 21 27 = 3b 9 = b Unit G

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