Question

HELP ME ASAP! I have this assignment as missing ahhhh!! I'll mark brainliest

In the right triangles shown, the measure of angle ABC is the same as the measure of angle EBD.


What is the length of side BE?

Answer 1

Answer:

$3\frac{1}{3}$

or

$\frac{10}{3}$

or

$3.333$

Step-by-step 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

$\frac{ac}{ab} = \frac{de}{be}$

Plug in the numbers.

$\frac{3}{5} = \frac{2}{x}$

Cross multiply

$3x = 10$

$x = \frac{10}{3}$

As a decimal it equal

$3.333$

or

$3\frac{1}{3}$