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Understanding Parallelograms: Definition, Properties, and Examples

A parallelogram is a quadrilateral with opposite sides that are parallel. It can be named using all four vertices in either clockwise or counterclockwise order, such as ABCD or ADCB. Key properties include that both pairs of opposite sides and angles are congruent, consecutive angles are supplementary, and diagonals bisect each other. This guide provides examples to illustrate these properties, along with exercises to reinforce understanding of measurements, angles, and relationships within parallelograms.

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Understanding Parallelograms: Definition, Properties, and Examples

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  1. Parallelograms MM1G3.d

  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:

  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 .

  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.)

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