Question

△efg and △ghi are shown below.
which statement is true?
△efg is similar to △ghi.
△efg is not similar to △ghi.
there is not enough information to determine whether the triangles are similar

Explanation:

Step1: Identify given info

We know that $\overline{EF} \parallel \overline{GH}$ and $\overline{FG} \parallel \overline{IG}$ (from the midpoint/parallel markers on the segments).

Step2: Corresponding angles are equal

By the Corresponding Angles Postulate:

• $\angle FEG = \angle HGI$
• $\angle EFG = \angle GIH$
• $\angle EGF = \angle GHI$

Step3: Apply AA similarity criterion

If all corresponding angles of two triangles are congruent, the triangles are similar by the Angle-Angle (AA) Similarity Theorem.

Answer:

$\triangle EFG$ is similar to $\triangle GHI$.