Question

Given: In ∆ABC below,BD/BA = BE = BC .
Prove: segment DE is parallel to segment AC

Which statement and reason can be used to fill in the numbered blank spaces?

Answer 1

Answer choices:

A. 1. ∡BDE ≅ ∡BAC
2. Corresponding Parts of Similar Triangles

B. 1. ∡BDE ≅ ∡BCA
2. Alternate Exterior Theorem

C. 1. ∡BDE ≅ ∡BAC
2. Corresponding Angles Postulate

D. 1. ∡BDE ≅ ∡BCA
2. Corresponding Parts of Similar Triangles

Answer 2

@jim_thompson5910
@.Sam.
@Hero

Can someone please help me understand this?

Answer 3

I kinda think it's B but i'm not quite sure

Answer 4

Oh God, I cringed when it came to proofs

Answer 5

@RICARDOismyfirstname .. You are trying to prove DE is parallel to AC. So you cannot use the Alternate Exterior Theorem. On to of that Angle BDE and Angle BCA line on different transversals altogether. So you cannot compare them.

Here the previous step to the blank space is you proved your triangles to be similar. Once you prove their similarity you have to use that and prove the next.

Answer choice B is ruled out because of my first argument. You cannot classify those angles as a pair.

Answer Choice B talks about Corresponding angle theorem which will follow the proof that DE is parallel to AC. So its not correct.

Answer Choice D . Angle BDE and Angle BCA are not corresponding parts of the similar triangle. So it is not correct.

Your answer is A. After proving the triangles to be similar, you prove the corresponding parts of the similar triangles are similar too.