Question

Fill in the missing statement and reason of the proof below.

Given: AABH AEDI and GH GI.
Prove: HGF ~ LIGF.

Answer 1

The missing statement is that ∠HGF ≅ ∠IGF, and the reason for this is that corresponding parts of congruent triangles are congruent.

The missing statement in the proof is:

5. ∠HGF ≅ ∠IGF

The reason for this statement is Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Here's why:

We are given that ΔABH ≅ ΔEDI (Step 1).

We are also given that ∠GH ≅ ∠GI (Step 2).

Since the triangles are congruent, their corresponding angles are congruent (CPCTC). Therefore, ∠HAB ≅ ∠IED (Step 3).

In Step 4, we are given that ∠A ≅ ∠E.

Combining Steps 3 and 4, we have ∠HAB + ∠A ≅ ∠IED + ∠E.

Simplifying the expression, we get ∠HAG ≅ ∠IFG.

Therefore, based on CPCTC, we can conclude that ∠HGF ≅ ∠IGF (Step 5).