   Chapter 5.2, Problem 34E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In the drawing, A B ↔   | |     D C ↔     | |       E F ↔ . Suppose that transversals l and m are also parallel. D and C are the midpoints of A E ¯ and B F ¯ , respectively. If parallelogram ABCD similar to parallelogram DCFE? To determine

To check:

Whether the parallelogram ABCD is similar to DCFE or not

Explanation

Given:

In the figure,

AB||DC||EF with transversals l and m. If D and C are the midpoints of AE¯ and BF¯.

Approach:

Two trapezoids are similar if and only if two conditions are satisfied:

1. Three or more parallel lines intercept congruent line segments on one transversal.

2. The intercept congruent line segments on any transversal.

Proof:

Let us consider the parallelograms, ABCD and DCFE.

Since AB||DC||EF, all pairs are parallel lines, intercept congruent line segments on one transversal.

That is, if two or more parallel lines intersect two transversals, l and m, then the parallel lines cut off the transversals proportionally

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