In the figure, and ∠eia ≅ ∠gjb. Complete the following statements to prove that ∠ikl ≅ ∠dlh. ∠eia ≅ ∠ikc and ∠gjb ≅ ∠jld because they are corresponding angles of parallel lines cut by a transversal. So, if ∠eia ≅ ∠gjb, then ∠ikc ≅ ∠jld by the. ∠ikl and ∠ikc and ∠dlh and ∠jld are pairs of supplementary angles by the. M∠ikl + m∠ikc = 180° (1) ∠ikc ≅ ∠jld, so m∠ikc = m∠jld (2) applying the to equations (1) and (2), we get m∠ikl + m∠jld = 180°. Therefore, ∠ikl and ∠jld are supplementary angles. We've already shown that ∠dlh and ∠jld are supplementary angles. Therefore, ∠ikl ≅ ∠dlh by the.