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Lesson 6-1

Parallelograms. Lesson 6-1. B. C. D. A. Parallelogram. Definition:. A quadrilateral whose opposite sides are parallel. A parallelogram is named using all four vertices. You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction.

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Lesson 6-1

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  1. Parallelograms Lesson 6-1 Lesson 6-1: Parallelogram

  2. B C D A Parallelogram Definition: A quadrilateral whose opposite sides are parallel. • A parallelogram is named using all four vertices. • You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction. • For example, the figure above can be either ABCD or ADCB. Symbol: a smaller version of a parallelogram Naming: Lesson 6-1: Parallelogram

  3. A B Properties of Parallelogram P D C 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other but are not congruent P is the midpoint of . Lesson 6-1: Parallelogram

  4. H K Examples M P L • Draw HKLP. • HK = _______ and HP = ________ . • m<K = m<______ . • m<L + m<______ = 180. • If m<P = 65, then m<H = ____,m<K = ______ and m<L =____. • Draw the diagonals with their point of intersection labeled M. • If HM = 5, then ML = ____ . • If KM = 7, then KP = ____ . • If HL = 15, then ML = ____ . • If m<HPK = 36, then m<PKL = _____ . PL KL P P or K 115° 115° 65 5 units 14 units 7.5 units 36; (Alternate interior angles are congruent.) Lesson 6-1: Parallelogram

  5. Sides and Angles Theorem 6.1: Opposite sides of a parallelogram are congruent.

  6. Sides and Angles Consecutive angles: angles of a polygon that share a side and are consecutive angles of a parallelogram. They are . Theorem 6.2: Opposite angles of a parallelogram are congruent.

  7. Diagonals and Transversals Theorem 6.3: The diagonals of a parallelogram bisect each other.

  8. Diagonals and Transversals

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