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