Question

In the right triangles shown, the measure of ange ABC is the same as the measure of ange EBD What is the length of

side BE
13
D3
E
5
С
Question 3 (2 points)

Answer 1

3 1/3

10/3

3.333

Explanation:

These two triangles are similar. Since they share two angles, the right angle and angle EBD and ABC are congruent. By AA similarity rule, they are similar triangles.

Since they are similar we can set up a proportion of the triangles since similar triangles have proportional side length.

Side AC corresponds with DE

Side AB corresponds with BE

Side BC corresponds with BD

So we can use this proportion theorem, or angle bisector theorem

`(ac)/(ab)=(de)/(be)`

Plug in the numbers.

`(3)/(5) =(2)/(x)`

Cross multiply

3x=10

x=10/3

Simplify is

3 1/3

As a decimal it equal 3.333