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6.2: Properties of Parallelograms

6.2: Properties of Parallelograms. Objectives: To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms or transversals. THEOREM:. Opposite sides of a parallelogram ( ) are congruent. Example: Given EFGH.

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6.2: Properties of Parallelograms

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  1. 6.2: Properties of Parallelograms Objectives: To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms or transversals

  2. THEOREM: Opposite sides of a parallelogram ( ) are congruent.

  3. Example: Given EFGH Find GH and EG 7 E F 6 G H

  4. Theorem: Opposite angles of a are congruent. W V T U

  5. EXAMPLE C J 115 65 G H FIND measure of angle J and angle H.

  6. Consecutive Angles • Angles that share a side D C A B

  7. In a parallelogram, consecutive angles are supplementary (Because they are same-side interior angles!!) D C A B

  8. Find the values of the variables. b+7 c+4 2c 60° (3a)° 18

  9. Theorem: The diagonals of a bisect each other. E F K H G Example: If EK = 4 and HK = 7, find KG and KF

  10. The figure below is a parallelogram. Find the value of x. A 2x-1 AD=26 D

  11. The figure below is a parallelogram. Find the values of x and y. 2x+3 6y-16 4y 4x-9

  12. Theorem: If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on EVERY transversal.

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