Write a two-column proof.

Question

If FG ⊥ IJ and IG ≅ JG, then FI ≅ FJ

Answer 1

If IJ intersects FG at M, then angles IMG and JMG are right angles

MG is common to both triangles IMG and JMG.

So, via the Pythagorean Theorem, IM ≅ JM.

Now use that last fact, along with the common side FM to show that triangles IMF and JMF are congruent.

That means that IF≅JF