Answers:
- Reason 1: Given
- Reason 2: Vertical Angles
- Reason 3: SAS Similarity Theorem
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Further Explanation:
Whenever you are doing a proof, always start with the given info. It may seem silly to literally repeat (word-for-word) what your teacher has given you, but this is how all proofs start out. It helps place an anchor point in which you can connect to what you want to prove.
So this is why the first line is literally a repeat of what your teacher has stated. The reason you'll state is "given".
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For reason 2, we use the vertical angle theorem. Vertical angles are always congruent.
Vertical angles form whenever we have an X shape like this of two segments crossing. The angles are opposite one another (almost like mirror images of sorts).
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Lastly, reason 3 uses the SAS (side angle side) similarity theorem.
This is the theorem which says that if you have two pairs of sides in proportion and a pair of congruent angles between those sides, then we can prove the triangles similar.
Statement 1 handles the sides being in proportion. Statement 2 handles the congruent angles.
As you can see, everything in this proof builds step by step toward the final goal of saying triangle ABC is similar to triangle EBD.