# Congruence and Similarity- Explain?

#### SpaghettNeo

Hello!

I took this test a week or two ago and wanted to go over all my wrong answers in preparation for another test coming up, but this problem seems to have no explanation as to how they got the answer 1600. Now, I realize since this is a congruency problem I have to do some kind of work with the congruent triangle in order to get the value of x, but how exactly do I go about this? Please explain as much as possible- thank you!

-Neo

#### SlipEternal

MHF Helper
First, prove that the two triangles are similar. Once they are similar, match up similar sides and angles. This will tell you that BD is similar to EB and CD is similar to AE. Since the ratio BD:EB = 1:2, the same is true for CD:AE.

2 people

#### Plato

MHF Helper
From the diagram we see that $\Delta ABE \approx \Delta CBD$.

From that notation we read off: $\dfrac{{AE}}{{EB}} = \dfrac{{CD}}{{DB}}$

2 people

#### SpaghettNeo

Thanks so much, I can't believe I didn't see that to begin with, it's so simple! So since we see that 700 x 2 = 1400 for EB/BD, we can also say that 800 x 2 = 1600 for CD/EA, correct?

Thanks again, your help is very appreciated!
-Neo