Question

Below are statements that can be used to prove that the triangles are similar.

On a coordinate plane, right triangles A B C and Z Y X are shown.
1. StartFraction A B Over Z Y EndFraction = StartFraction B C Over Y X EndFraction = 2

2. ∠B and ∠Y are right angles.

3.?

4.?

Which two statements are missing in steps 3 and 4?

∠X ≅ ∠C
△ABC ~ △ZYX by the SAS similarity theorem.
∠B ≅ ∠Y
△ABC ~ △ZYX by the SAS similarity theorem.
StartFraction A C Over X Y EndFraction = 2
△ABC ~ △ZYX by the SSS similarity theorem.
StartFraction Z X Over A C EndFraction = 2
△ABC ~ △ZYX by the SSS similarity theorem.

Answer 1

Step 3: ∠B ≅ ∠Y
Step 4: △ABC ~ △ZYX by the SAS similarity theorem

Reason: AB/ZY = BC/YX and the included angles ∠B and ∠Y are right, so two sides are proportional and the included angles are congruent → SAS similarity.