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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 25 to 28, Δ A B C Δ D B E

Chapter 5.3, Problem 26E, In Exercises 25 to 28, ABCDBE Exercises 25-28 Given: AC = 10, CB = 12. E is the midpoint of CB Find:

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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