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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Quadrilateral E F G H has the vertices E 0 ,   0 , F a ,   0 , G a + b ,   c , and H 2 b , 2 c . Verify that E F G H is a trapezoid by showing that the slopes of two sides are equal.

Chapter 10.2, Problem 41E, Quadrilateral EFGH has the vertices E0,0, Fa,0, Ga+b,c, and H2b,2c. Verify that EFGH is a trapezoid

To determine

To prove:

The quadrilateral EFGH is trapezoid by showing the slopes of two sides are equal.

Elementary Geometry for College Students, Chapter 10.2, Problem 41E

Explanation

To prove that the quadrilateral is a trapezoid, one of the opposite sides must be parallel,

By theorem,

If two lines are parallel, then their slopes are equal.

(i.e) If l1l2, then m1=m2.

So we can prove this by using the slopes.

Thus we have to prove the line EH is parallel to the line FG.

The slope of the line that contains the points x1,y1 and x2,y2 is given by

m=y2-y1x2-x1 for x2x1

Let mEH- and mFG- are the slopes of the line EH- and FG- respectively.

The given vertices are E0, 0, and H2b, 2c.

Using the slope formula and choosing x1=0, x2=2b, y1=0, and y2=2c

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