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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 4 Page 526

A trapezoid is isosceles if its non-parallel sides are congruent.

ABCD is an isosceles trapezoid.

Practice makes perfect

Let's begin by plotting the given vertices and drawing the quadrilateral on a coordinate plane.

In the previous exercise we already found that ABCD is a trapezoid. A trapezoid is isosceles if its non-parallel sides are congruent. Therefore, we want to check whether the lengths of AB and CD are equal. To do this, we will use the Distance Formula.

Side	Distance Formula	Simplified
Length of AB: ( -4,-1), ( -2,3)	sqrt(( -2-( -4))^2+( 3-( -1))^2)	sqrt(20)
Length of CD: (3,3), (5, - 1)	sqrt((5-3)^2+(-1-3)^2)	sqrt(20)

Since the lengths are equal, legs AB and CD are not congruent. Therefore, trapezoid ABCD is isosceles.

Subchapter links

Exercises p.526-530