Question

Prove AFGH= AHIF. F G 1) FI = GH 2) FH = FH 3) ZGFH=/IHF 4) AFGHAHIF ANDE I H Statements 1) 2) 3) 4) Reasons​

Answer 1

By SAS criterion ∆FGH ≅ ∆HIF.

What is congruence?

Congruent triangles share identical shape and size. They can be proven congruent by satisfying criteria such as Side-Angle-Side, Side-Side-Side, Angle-Side-Angle, Angle-Angle-Side, or Hypotenuse-Leg, establishing corresponding equalities in sides and angles between the triangles.

To prove ∆FGH ≅ ∆HIF

Proof:

1) FI ≅ GH (Given)

2) FH ≅ FH (Reflective property of congruence)

3) ∠GFH ≅ ∠IHF (Given)

4) ∆FGH ≅ ∆HIF(Side-Angle-Side SAS)

Therefore, by SAS criterion ∆FGH ≅ ∆HIF.