Exercise 26 Page 588

Let's consider the right triangle △ GHJ where K, L, and M are the midpoints of each sides.

Notice that both KL and KM are midsegments of △ GHJ. We can apply the Triangle Midsegment Theorem.

From the above we get that KLHM is a parallelogram.

Then, by the Parallelogram Opposite Angles Theorem we conclude that ∠ H ≅ ∠ LKM. Since ∠ H is a right angle we get that ∠ LKM is a right angle as well, and this is what we wanted to prove.

Two-Column Proof

Given: & ∠ H a right angle & L, K, and M are midpoints Prove: & ∠ LKM is a right angle We will summarize the proof we did above in the following two-column table.