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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.