Geometry Section 8.2.

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Presentation transcript:

Geometry Section 8.2

Parallelograms By definition, a Parallelogram is a quadrilateral that has two pairs of parallel sides.

What are some properties of the parallelogram seen in the quilt below?

EXAMPLE 1 Use properties of parallelograms ALGEBRA Find the values of x and y. ABCD is a parallelogram by the definition of a parallelogram. In ABCD, x = 8 and y = 65. ANSWER

EXAMPLE 2 Use properties of parallelograms Desk Lamp As shown, part of the extending arm of a desk lamp is a parallelogram. The angles of the parallelogram change as the lamp is raised and lowered. Find m BCD when m ADC = 110°.

EXAMPLE 3 Standardized Test Practice SOLUTION By Theorem 8 .6, the diagonals of a parallelogram bisect each other. So, P is the midpoint of diagonals LN and OM . Use the Midpoint Formula. = Coordinates of midpoint P of OM 4 + 0 2 7 + 0 , ( ) = 7 ( ) The correct answer is A. ANSWER

Find the missing variables.