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6.6 – Special Quadrilaterals

6.6 – Special Quadrilaterals. What kind of quadrilateral is it?. Possible answers: Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezoid To Decide which: Graph the answer. If all sides are congruent: Rhombus (maybe square) ‏ If all angles are perpendicular: Rectangle (maybe square) ‏

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6.6 – Special Quadrilaterals

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  1. 6.6 – Special Quadrilaterals

  2. What kind of quadrilateral is it? • Possible answers: Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezoid • To Decide which: Graph the answer. • If all sides are congruent: Rhombus (maybe square)‏ • If all angles are perpendicular: Rectangle (maybe square)‏ • See previous notes for other properties

  3. Example • What kind of quadrilateral is at C(2,5), O(6,3), L(2,1), and D(-2, 3)‏ • How do you know?

  4. Solution • Graph looks like a rhombus – all the sides must be congruent (and opposite side parallel). Use the distance formula to prove.

  5. Solution Cont’d • Pairs of sides must be parallel • Slopes of opposite sides should be equal • M = (y2 – y1)/(x2 – x1) • CO = (3-5)/(6-2) = -2/4 = - ½ • OL = (1-3)/(2-6) = -2/-4 = ½ • LD = (3-1)(-2-2) = 2/-4 = - ½ • DC = (5-3)/(2 - -2) = 2/4 = ½ • Yes, the pairs are parallel • If you need to prove that sides are perpendicular (rectangle, square), the slopes must be negative reciprocals)

  6. Assignment • p. 368 16-24, 36-41all

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