Question

In the figure, AB║CD and ∠EIA is congruent to ∠GJB Complete the following statements to prove that ∠IKL is congruent to ∠DLH.

Answer 1

Here it is given that AB || CD

< EIA = <GJB

Now

∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)

∠EIA  ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)

∠IKL + ∠IKC 180° and ∠DLH +  ∠JLD =180° (Linear Pair Theorem)

So

m∠IKL + m∠IKC = 180°       ....(1)

But ∠IKC  ≅ ∠JLD

m∠IKC = m∠JLD (SUBTRACTION PROPERTY OF CONGRUENCY)

So we have

m∠IKL + m∠JLD = 180°

∠IKL and ∠JLD are supplementary angles.

But ∠DLH and ∠JLD are supplementary angles.

∠IKL ≅ ∠DLH (CONGRUENT SUPPLEMENTS THEOREM)

Answer 2

The answers 
1)  D. (TRANSITIVE PROPERTY OF CONGRUENCY)
2)  C. (LINEAR PAIR THEOREM)
3)  D. TRANSITIVE PROPERTY OF CONGRUENCY) to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.
4)  C. (CONGRUENT SUPPLEMENTS THEOREM)