Question

Look at the figure.
Make a two-column proof showing statements and reasons to prove that triangle ABD is similar to triangle ABC.

Answer 1

@ganeshie8

Answer 2

@phi

Answer 3

what ways do you know to show 2 triangles are congruent?

Answer 4

ASA postulate?

Answer 5

@phi

Answer 6

Sorry, I was called away.

Re-reading the question, they want to show the triangles are similar

to be similar we need to show their 3 angles are congruent.
actually, if 2 angles out of the 3 are congruent, then so is the 3rd
(because the 3rd angle is 180 - sum of the other two )

so the proof would be like this:
statement reason
<ABD = <ABC Given (in the figure)
<BAD = <BAC angle equals itself (reflexive property)
<ADB = <ABC if 2 angles are congruent then so are the 3rd angles
Triangle ABD is similar to Triangle ABC corresponding angles are congruent