   Chapter 5.3, Problem 26E 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 Exercises 25 to 28, Δ A B C ∼ Δ D B E Exercises 25-28 Given: AC = 10, CB = 12.E is the midpoint of C B ¯ Find: DE

To determine

To find:

The side DE when the given sides are AC = 10, CB = 12, E is the midpoint of CB¯

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

That is, BDBA=BEBC=DEAC.

It is given that AC = 10, CB = 12, E is the midpoint of CB¯.

From Figure 1, it is noticed that E is the midpoint of CB¯ means E=12CB

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