   Chapter 5.3, Problem 30E 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

Δ C D E ∼ Δ C B A with ∠ C D E ≅ ∠ B . If C D = 10 , C A = 16 and E B = 12 , find CE. Exercises 29, 30

To determine

To find:

The side CE by using the given information.

Explanation

Definition:

CSSTP:

Corresponding sides of similar triangles are proportional.

Description:

Given that ΔCDEΔCBA with CDEB. If CD=10,CA=16 and EB=12.

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 ΔCDEΔCBA and from the definition of CSSTP, corresponding sides of similar triangles are proportional.

That is, CDCB=CECA=DEBA.

It is given that CD=10,CA=16 and EB=12.

Find the side CE.

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

From Figure 1, it is observed that CB=CE+EB

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