It is given that ∠EIJ ≅ ∠GJI. Also, ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK, as they are corresponding angles for parallel lines cut by a transversal. By the definition of congruent angles, m∠EIJ = m∠GJI, m∠EIJ = m∠IKL, and m∠GJI = m∠JLK. So, m∠IKL = m∠JLK by the . Angle JLK and ∠JLD are supplementary angles by the , so m∠JLK + m∠JLD = 180°. By the , m∠IKL + m∠JLD = 180°. Therefore, ∠IKL and ∠JLD are supplementary angles by definition.