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6-3 Proving Parallelograms

6-3 Proving Parallelograms. Ways to prove parallelogram (theorems). If diagonals bisect each other then a quad is a parallelogram If both pairs of opposite sides are congruent then a quad is a parallelogram If both pairs of opposite angles are congruent then a quad is a parallelogram.

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6-3 Proving Parallelograms

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  1. 6-3 Proving Parallelograms

  2. Ways to prove parallelogram(theorems) • If diagonals bisect each other then a quad is a parallelogram • If both pairs of opposite sides are congruent then a quad is a parallelogram • If both pairs of opposite angles are congruent then a quad is a parallelogram

  3. Ways to prove parallelogram(theorems) • If one pair of opposite sides are both parallel and congruent then a quad is a parallelogram

  4. Examples Find the values of the variables for which GHIJ must be a parallelogram. 1) 2)

  5. Examples Determine whether the quadrilateral must be a parallelogram. Explain. 3) 4) 5)

  6. Examples Is the given info enough to prove the quad is a parallelogram? Explain. 6) BC ≅ AD & BA ≅ CD 7) <BAD ≅ <BCD & <ABC ≅ <ADC 8) AB ≅ CD & BC || AD 9) BE ≅ ED & EA ≅ EC 10) BC ≅ AD & BC || AD

  7. Honors: Proof Statements Reasons 1 2 3 4

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