Question

Triangles F G H and J K L are shown. Angles G F H and K J L are congruent and angles F H G and J L K are congruent.
To show that ΔFGH ≅ ΔJKL by SAS, what additional information is needed? Check all that apply.

FH ≅ JL and FG ≅ JK
FH ≅ JL and HG ≅ LK
∠G ≅ ∠K and FH ≅ JL
∠G ≅ ∠K and GH ≅ KL
∠G ≅ ∠K and FG ≅ JK

Answer 1

Choose FH ≅ JL and either FG ≅ JK or GH ≅ KL.

Reason: The given congruent angles are ∠F ≅ ∠J and ∠H ≅ ∠L, so the included side FH must equal JL. For SAS you then need one more pair of corresponding sides adjacent to that included angle: either FG ≅ JK (use ∠F) or GH ≅ KL (use ∠H). Thus options 1 and 2.