Prove the following indirectly using two-column form:

Question

Given: Segment GK ≢ (not equal) segment HI, ∠K ≅ ∠H

Prove: Segment JK ≢ (not equal) segment HJ

Answer 1

Triangle HIJ and triangle GJK are similar because the angles are equal (angle K=angle H is given, the vertical angles are equal therefore the 3rd angles of each triangle are equal).

Set up the proportion and your answer will stare you in the face!

I haven't given you a so-called 2 column proof, but I have given you what you need to do that.