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Understanding Parallelograms: Properties and Examples in Geometry

This lesson on parallelograms covers their definition, properties, and naming conventions. A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel and congruent. It can be named using its four vertices in a clockwise or counterclockwise direction. Key properties include congruent opposite sides and angles, supplementary consecutive angles, and bisecting diagonals. Examples are provided to illustrate these properties and to solve related problems involving angles and segment lengths within parallelograms.

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Understanding Parallelograms: Properties and Examples in Geometry

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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

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