Find the slope of each of the four sides and look for equal slopes. If Both Pairs of Opposite Sides Are parallel, then The quadrilateral Is a By Definition.

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Presentation transcript:

Find the slope of each of the four sides and look for equal slopes. If Both Pairs of Opposite Sides Are parallel, then The quadrilateral Is a By Definition of a parallelogram. Parallelogram. Q (-8, 5), U ( 0, 11), A (6, 3), D (-2, -3) Slope of QU Slope of UA Slope of ADSlope of QD

That is also a Find the slope of each of the four sides and compare adjacent sides. Q (-8, 5), U ( 0, 11), A (6, 3), D (-2, -3) Slope of QU =Slope of UA = Slope of AD =Slope of QD = We now have aParallelogram.Rectangle.

We now have a that is also a And now it is also a. ParallelogramRectangle. Find the slope of the two diagonals and compare. Q (-8, 5), U ( 0, 11), A (6, 3), D (-2, -3) Slope of QA = Slope of UD = Rhombus

Now we have shown that this Is both a and a So, it must follow that it is also a Parallelogram Rectangle Q (-8, 5), U ( 0, 11), A (6, 3), D (-2, -3) Rhombus SQUARE

S U M M A R Y If both pairs of opposite sides have the same slope then it is a Parallelogram. If the product of the slopes of the adjacent sides is equal to negative 1, then it is a Rectangle. If the product of the slopes of the diagonals is equal to negative 1, then it is a Rhombus. If it is both a Rectangle and a Rhombus, then it is also a SQUARE.

Parallelogram Rectangle. You try this one!! M (-9, 2), A ( 3,7), T (15, 2), H (3, -3) Slope of MA = (7-2)/(3- -9)=5/12 Slope of AT = (2- 7)/(15- 3)=- 5/12 Rhombus Slope of TH = (- 3- 2)/(3 -15)= - 5/-12 = 5/12 Slope of HM = (- 3- 2)/(3- -9)=- 5/12 Slope of MT = (2- 2)/(15- -9)= 0/24 = 0 Slope of AH = (- 3- 7)/(3- 3)=- 10/0 = undefined Square This one is a Parallelogram and a Rhombus. 5/12 (- 5/12)  -1

If the quadrilateral is not a Parallelogram, then it is not a Rectangle, Rhombus or Square. If the quadrilateral is not a Rectangle then it is not a Square. If the quadrilateral is not a Rhombus then it is not a Square.

If there are two pair of adjacent sides that are congruent and opposite sides are not congruent, then you have a Kite. The diagonals will also be perpendicular with one bisecting the other, but not vice versa. But what if it is not a parallelogram? Could it be a Trapezoid? Or a Kite? If one pair of sides are parallel and the other pair is not, then you have a Trapezoid. If the nonparallel sides (legs) are congruent, then it is also an Isosceles Trapezoid. If there are two pair of adjacent sides that are congruent and opposite sides are not congruent, then you have a Kite. The diagonals will also be perpendicular with one bisecting the other, but not vice versa.