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6-2 Properties of Parallelograms

Explore the theorems and proofs concerning parallelograms, learn how to find their areas, and solve geometric problems related to angles and sides.

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6-2 Properties of Parallelograms

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  1. 6-2 Properties of Parallelograms

  2. Area • Area of Parallelogram • A = base x height

  3. 2. 3. 4. 5. 6. 7. 8. Proof

  4. 1. 2. 3. 4. 5. 6. 7. Proof

  5. Theorems Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Consecutive angles of a parallelogram are supplementary. Diagonals of a parallelogram bisect each other.

  6. Theorems If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  7. 1) Find area of the parallelogram 2) Find area of a parallelogram with vertices (-5,-3), (-2,3), (2,3) & (-1,-3). Examples

  8. Examples 3) If AB=3x + 11, BC = 2x + 19 and CD = 7x – 17, find x. 4) If m<BAD = y and m<ADC = 4y – 70, find y. 5) If m<ABC=2x + 100 and m<ADC=6x + 84, find m<BCD.

  9. Examples • 6) If m<BCD=80 and m<CAD=34, find m<ACD. • 7) If AP=3x, BP=y, CP=6x - 42, and DP=27 - 2y, find x &y.

  10. Examples 8) Find EH.

  11. Example: Honors Geometry Statements Reasons 1. 2. 3. 4. 5. 6.

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