The proof that ΔEFG ≅ ΔJHG is shown.

Question

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

To fill in the missing statement in the proof, we need to focus on the property involving the parallel lines.

Since EF is parallel to HJ (according to statement 3), the alternate interior angles formed by the transversal line FG must be congruent. Therefore, the correct missing statement is:

∠FEG ≅ ∠HJG

So, the final proof with the missing statement included would look like this:

1. G is the midpoint of HF. 1. Given
2. FG ≅ HG. 2. Definition of midpoint
3. EF ∥ HJ. 3. Given
4. ∠FEG ≅ ∠HJG. 4. Alternate interior angles are congruent
5. EF ≅ HJ. 5. Given
6. ΔEFG ≅ ΔJHG. 6. SAS (Side-Angle-Side)

This confirms that triangles EFG and JHG are congruent.