Question

Given: HF || JK; HG ≅ JG
Prove: TriangleFHG ≅ TriangleKJG

Triangles F H G and K J G connect at point G. Sides F H and J K are parallel. Sides H G and G J are congruent.
To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

AngleFGH ≅ AngleKGJ because vertical angles are congruent.
AngleJKG ≅ AngleHFG because vertical angles are congruent.
AngleFHG ≅ AngleJKG because right angles are congruent.
AngleHFG ≅ AngleKJG because alternate interior angles are congruent.

Answer 1

Angle HFG ≅ Angle KJG, because HF ∥ JK so those are alternate interior angles.

(With HG ≅ JG and the vertical angles at G congruent, this gives the two angles and the included side — ASA — so ΔFHG ≅ ΔKJG.)