given: segment HI congruent to segment GJ, segment HI parallel to segment GJ

Question

prove: triangle GJH congruent to triangle IHJ

Answer 1

Proof:
Since segment HI is congruent to segment GJ and parallel to segment GJ, then angles HGI and IHJ are congruent.
Since angles HGI and IHJ are congruent, then sides GH and IJ are congruent.
Since sides GH and IJ are congruent, then angles GHI and IJH are congruent.
Since angles GHI and IJH are congruent, then triangle GJH is congruent to triangle IHJ.
Therefore, triangle GJH is congruent to triangle IHJ.