Question

The proof that ΔEFG ≅ ΔJHG is shown.

Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ.

Prove: ΔEFG ≅ ΔJHG

Triangles E F G and J H G share common point G.


Statement

Reason
1. G is the midpoint of HF 1. given
2. FG ≅ HG 2. def. of midpoint
3. EF ∥ HJ 3. given
4. ? 4. alt. int. angles are congruent
5. EF ≅ HJ 5. given
6. ΔEFG ≅ ΔJHG 6. SAS
What is the missing statement in the proof?

∠FEG ≅ ∠HJG
∠GFE ≅ ∠GHJ
∠EGF ≅ ∠JGH
∠GEF ≅ ∠JHG

Answer 1

∠GFE ≅ ∠GHJ

Reason: EF ∥ HJ and line FG (collinear with HF) is a transversal, so the alternate interior angles at F and H are congruent. With FG ≅ HG and EF ≅ HJ, SAS gives ΔEFG ≅ ΔJHG.