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Section 5-1

Parallelograms. Section 5-1. B. C. D. A. Parallelogram. Definition:. A quadrilateral with both pairs of opposite sides 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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Section 5-1

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  1. Parallelograms Section 5-1

  2. B C D A Parallelogram Definition: A quadrilateral with both pairs of opposite sides 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. *** Remember: a smaller version of a 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. 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° 65 115° 5 units 14 units 7.5 units (Alternate interior angles are congruent.) 36;

  5. Examples • ABCD is a parallelogram. Find the values of x, y, and z.

  6. More examples…

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