Question

Triangle GHI is dilated to create triangle JKL on a coordinate grid. You are given that angle H is congruent to angle K. What other information is required to prove that the two triangles are similar?​

Answer 1

Answer:  a) ∠I = ∠L

Step-by-step explanation:

Since we are trying to prove Similarity, we can use Angle-Angle (AA) Similarity Theorem which states that if two angles are congruent, then the triangles are similar.

We can also use Side-Angle-Side Similarity Theorem which states that if the sides are PROPORTIONAL to each other (not equal) and the included angle is congruent then the triangles are similar.

G H I

J K L

Given: ∠H = ∠K

a) ∠I = ∠L      

This can be used to prove ΔGHI ≅ ΔJKL by Angle-Angle (AA) Similarity Theorem

b) GI = JL and HI = KL

This can be used to prove ΔGHI ≡ ΔJKL by Side-Angle-Side (SAS) Congruency Theorem, however it was stated that there was a dilation so we know that the sides will not be congruent. We are looking for similarity so those sides would need to be proportional to each other (not equal).

c) ∠H = ∠J

If you look at the order of the letters, H and J are not in the same position so we cannot use this to prove either similarity or congruency.

d) GH = JK

This only gives us one side and one given angle which is not enough information to prove either similarity or congruency.