Chapter 5.3, Problem 40E

### 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 the figure, ∠ A B C ≅ ∠ A D B . Find AB if A D = 2 and D C = 6 .

To determine

To find:

The length of the side AB if the given sides are AD = 2, DC = 6 and ABCADB.

Explanation

Definition:

AA:

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

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 ADB.

Now draw the two triangles separately as shown below.

Figure 2

Figure 3

Given that âˆ ABCâ‰…âˆ ADB and the point A is common for both the triangles. So by identity âˆ Aâ‰…âˆ A.

From the above mentioned AA definition, the two triangles ABC and ADB are similar since the two angles of one triangle are congruent to two angles of another triangle. Hence, Î”ABCâˆ¼Î”ABD.

From the definition of CSSTP, corresponding sides of similar triangles are proportional.

It is given that ADÂ =Â 2,Â DCÂ =Â 6

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