Page 164 - ArithBook5thEd ~ BCC

In the examples and exercises, it will be convenient to use the following symbolism:

∥←→ “is parallel to”
∼ ←→ “is similar to”
△ ←→ “triangle”

Example 204. In the picture below, AB ∥ CD. Some of the side lengths are given in inches. Find the
length of the side AE.
A

C
1
E

.75
1.5
B D

Solution. Because AB ∥ CD, △ABE ∼△CDE. Corresponding sides are proportional, hence

smaller triangle CD EC ED
= = .
bigger triangle AB EB EA
In particular, using EC =1, EB =1.5, and ED =.75, and x for the length of AE,

1 .75
=
1.5 x

or x =(1.5)(.75) =1.125. The length of AE is 1.125 inches.

Example 205. In the following figure, DE ∥ BC.Find the length of BC.

A

2ft.

D E
2ft. 6in.
2ft. 4in.

B C

Page 164