Question

The ratios of corresponding sides in the two triangles are equal.

Triangles F G E and I J H are shown. The length of side G F is 15 and the length of side I J is 10. The length of F E is 30 and the length of I H is 20.

What other information is needed to prove that △FGE ~ △IJH by the SAS similarity theorem?

∠F ≅ ∠J
∠I ≅ ∠F
∠E ≅ ∠H
∠G ≅ ∠I

Answer 1

∠I ≅ ∠F.

Reason: GF and FE correspond to IJ and IH, respectively, and meet at F and I, so the included angles must be congruent; with the two pairs of side ratios equal and the included angles equal, the triangles are similar by SAS similarity.