Chapter 5.3, Problem 29E

### 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

# Δ C D E ∼ Δ C B A with ∠ C D E ≅ ∠ B . If C D = 10 , D A = 8 and C E = 6 , find EB.Exercises 29, 30

To determine

To find:

The side EB by using the given information.

Explanation

Definition:

CSSTP:

Corresponding sides of similar triangles are proportional.

Description:

Given that Î”CDEâˆ¼Î”CBA with âˆ CDEâ‰…âˆ B. If CD=10,DA=8 and CE=6.

The given figure is shown below.

Figure 1

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

Now draw the two triangles separately as shown below.

Figure 2

Figure 3

Since Î”CDEâˆ¼Î”CBA and from the definition of CSSTP, corresponding sides of similar triangles are proportional.

That is, CDCB=CECA=DEBA.

It is given that CD=10,DA=8 and CE=6.

Find the side EB.

Consider the first two pairs of proportions CDCB=CECA in order to find EB.

From Figure 1, it is observed that CA=CD+DA

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