The proof that ΔEFG ≅ ΔJHG is shown.

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

Prove: ΔEFG ≅ ΔJHG

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?

A. ∠FEG ≅ ∠HJG

B. ∠GFE ≅ ∠GHJ

C. ∠EGF ≅ ∠JGH

D. ∠GEF ≅ ∠JHG

SAS Postulate: If two sides and the included angle of the first triangle are congruent to the corresponding parts of the second triangle, then the correspondence is a congruence.

You have:

step 2 - FG ≅ HG (by the definition of midpoint);
step 5 - EF ≅ HJ (given)

So if you want to use SAS Postulate you have to prove that ∠EFG≅∠JHG. These angles are alternate interior angles at parallel lines EF and GH (given that they are parallel in step 3) and transversal FH.

Thus,

step 4 - when the two lines being crossed are parallel lines the alternate interior angles are congruent.

Therefore, you can use SAS in step 6.

ap8997154 ap8997154 · Answer 2 · 2022-02-22T10:50:01+01:00

Alternate Interior angles are opposite to each other. The missing statement in the proof is ∠FEG ≅ ∠HJG.

What are the alternative interior angles?

When two parallel lines are cut by a transverse then the angles formed on the inner side of the lines are opposite to each other are congruent to each other.

The two lines EF and HJ in ΔEFG and ΔJHG are parallel to each other, while the line EJ is the transverse to the two lines, therefore,

∠FEG ≅ ∠HJG

Hence, the missing statement in the proof is ∠FEG ≅ ∠HJG.

Learn more about Alternate Interior Angles:

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