In the figure, AB || CD and ∠EIJ ≅ ∠GJI. Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles.
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.