4/16/2017 Parallelograms.

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Presentation transcript:

4/16/2017 Parallelograms

Parallelogram Definition: 4/16/2017 Definition: A quadrilateral with both pairs of opposite sides parallel. C B A D The symbol for parallelogram is a smaller version of the figure. 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.

Properties of Parallelogram 4/16/2017 Properties of Parallelogram A B 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 AC and BD, so BP = PD and AP = PC.

4/16/2017 H Examples K 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 (Alternate interior angles are congruent.) 14 units 7.5 units 36°

Examples ABCD is a parallelogram. Find the values of x, y, and z. 4/16/2017 Examples ABCD is a parallelogram. Find the values of x, y, and z.

Example 2: In GEOM, EA = 2x2 + 5x and AM = 4x + 2. Find the value of x Example 2: In GEOM, EA = 2x2 + 5x and AM = 4x + 2. Find the value of x. What are EA and AM? G M A E O

Example 3. Given TRAC. If TC = 3x - 5 and RA = 25, solve for x. 4 K 1 2 If m∠CTR = 2y - 13 and m∠ACT = y + 1. Find y. C A

Example 4