How do I prove these two triangles are similar ?

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Zulgok

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I need to prove that triangles DBC and DFC are similar. I know one reason they are similar is because of shared DC. I have an idea of another reason, that the angle of DCF is equal to BDC. Am I wrong ? If not, what would be the explanation for it ? Thanks !
 
No angle is established. How do you know anything about the angles? Are there some Right Angles that could be labeled? Please present the ENTIRE problem and show your best work on the matter.
 
Yes, all of them are Right triangles. Also, forgot to mention that AB is 2 and BC is 1, so DB is root of 5. The only similarities I found between these two triangles is that they both are Right and CD is shared.
 
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Zulgok said:
View attachment 8631

I need to prove that triangles DBC and DFC are similar. [ . . . . ] I have an idea of another reason, that the angle of DCF is equal to BDC. What is your reason/justification?

Am I wrong ? If not, what would be the explanation for it ? Thanks !
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You have a right angle in each of those two triangles.

What do you conclude about the remaining two corresponding angles?
 
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