Exercise 38 Page 371

We will begin by highlighting the congruent angles in the given diagram, and also we will label ∠ LMJ.

Using that ∠ LMJ and ∠ KLM are supplementary, we can write the equation below. m ∠ LMJ + m ∠ KLM = 180 Since ∠ MJK ≅ ∠ KLM we have that m ∠ MJK = m ∠ KLM. Let's substitute it in the equation above. m ∠ LMJ + m ∠ MJK = 180 The latter equation tells us that ∠ LMJ and ∠ MJK are supplementary, and from the diagram we know they are consecutive interior angles.

Consequently, by applying the Converse of Consecutive Interior Angles Theorem we obtain that KJ ∥ LM.

Two-Column Proof

In the following table we summarize the proof we did above.