CK-12 Geometry - Second Edition

8.3. Using Similar Right Triangles http://www.ck12.org

Solution:Ifm^6 E= 30 ◦, thenm^6 I= 60 ◦andm^6 T RE= 60 ◦.m^6 IRT= 30 ◦because it is complementary to^6 T RE.
Line up the congruent angles in the similarity statement. 4 IRE∼4IT R∼4RT E

We can also use the side proportions to find the length of the altitude.

Example 2:Find the value ofx.

Solution:First, let’s separate the triangles to find the corresponding sides.

Now we can set up a proportion.

shorter leg in 4 EDG

shorter leg in 4 DF G

=

hypotenuse in 4 EDG

hypotenuse in 4 DF G

6

x

=

10

8

48 = 10 x

4. 8 =x

Example 3:Find the value ofx.