Question

what is the reason for the last step in the given proof? a. substitution property of equality b. linear pair theorem c. congruent supplements theorem d. transitive property of equality e. for parallel lines cut by a transversal, corresponding angles are congruent. proof: statement reason ∠eij≅∠gji given m∠eij = m∠gji definition of congruent angles ∠eij and ∠jik are supplementary linear pair theorem m∠eij + m∠jik = 180° definition of supplementary angles m∠gji + m∠jik = 180° substitution property of equality ∠gji and ∠jik are supplementary definition of supplementary angles ∠gji and ∠lij are supplementary linear pair theorem ∠jik≅∠lij

Explanation:

The Congruent Supplements Theorem states that if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. In the proof, ∠JIK and ∠LJL are both supplements of ∠GJI, so by the Congruent Supplements Theorem, ∠JIK≅∠LJL.

Answer:

C. Congruent Supplements Theorem