Then: You recognized and applied properties of parallelograms. Now: Recognize the conditions that ensure a quadrilateral is a parallelogram. 6.3 TEST FOR.

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

Then: You recognized and applied properties of parallelograms. Now: Recognize the conditions that ensure a quadrilateral is a parallelogram. 6.3 TEST FOR PARALLELOGRAMS

CONDITIONS FOR PARALLELOGRAMS

Theorem 6.10 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If  A  C and  B  D, then ABCD is a parallelogram. CONDITIONS FOR PARALLELOGRAMS

Determine whether each quadrilateral is a parallelogram. Justify your answer. a.b. c.d. EXAMPLE 1: IDENTIFY PARALLELOGRAMS

MECHANICS Scissor lifts, like the platform lift shown, are commonly applied to tools intended to lift heavy items. In the diagram,  A   C and  B   D. Explain why the consecutive angles will always be supplementary, regardless of the height of the platform. EXAMPLE 2: USE PARALLELOGRAMS TO PROVE RELATIONSHIPS

Find x and y so that the quadrilateral is a parallelogram. a. b. EXAMPLE 3: USE PARALLELOGRAMS AND ALGEBRA

Use the Distance, Slope and Midpoint Formulas to test if a quadrilateral is a parallelogram. a. Determine whether ABCD is a parallelogram by using the slope formula. A(0,0) B(1,3) C(5,3) D(4,0) EXAMPLE 4: PARALLELOGRAMS AND COORDINATE GEOMETRY

b. Determine whether ABCD is a parallelogram by using the distance and slope formula. (Hint: Pick one pair of sides) A(-3,2) B(-1,4) C(2,1) D(0,-1) EXAMPLE 4: PARALLELOGRAMS AND COORDINATE GEOMETRY

p #9-14 all, all, 24, 26, 3 40, 42, evens Graph #24,26, & ASSIGNMENT