Chapter 5.3, Problem 25E

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

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

In Exercises 25 to 28, Δ A B C ∼ Δ D B E Exercises 25-28Given AC = 8, DE = 6, CB = 6.Find: EB(HINT: Let EB = x, and solve an equation.)

To determine

To find:

The side EB when the given sides are AC = 8, DE = 6, CB = 6 and ΔABCΔDBE.

Explanation

Definition:

CSSTP:

Corresponding sides of similar triangles are proportional.

Description:

The given figure is shown below.

Figure 1

From the given figure, it is observed that there are two triangles ABC and DBE and which is given that two triangles are similar.

Now draw the two triangles separately as shown below.

Figure 2

Figure 3

Since Î”ABCâˆ¼Î”DBE and from the definition of CSSTP, corresponding sides of similar triangles are proportional.

That is, BDBA=BEBC=DEAC.

It is given that AC = 8, DE = 6, CB = 6.

Find the side EB.

Consider the last two pairs of proportions BEBC=DEAC in order to find EB

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