   Chapter 5.CT, Problem 6CT 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 right triangle A B C ,   C D - is the altitude from C to hypotenuse A B - . Name three triangles that are similar to each other. To determine

To find:

The triangles that is similar to each other.

Explanation

Given,

A right triangle ABC,CD¯ is the altitude from C to hypotenuse AB¯.

Here, the altitude cd¯ is drawn to the hypotenuse of a right triangle ABC that separates the right triangle into two right triangles as ADC,CDB

Therefore, we have the smaller triangles as follows,

Consider the ABC,ACD

Here, AA

BC

CD

AAA Theorem:

If the three angles of one triangle are congruent to the three angles of a second triangle then the triangles are similar.

Therefore by the above theorem

ABC~ACD

Consider the ABC,CBD

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