Next, since △ LKP and △ LMP are right triangles, we can apply the Hypotenuse-Leg Congruence Theorem to conclude that these triangles are congruent.
△ LKP ≅ △ LMP
↙ ↘
LK ≅ LM ∠ KPL ≅ ∠ MPL
We can conclude that L is the midpoint of KM and that JP bisects KM. Also, by the definition of arc measure, we can write the following two equations.
mKJ = m∠ KPL
mJM = m∠ MPL
Since the measures written on the right-hand side are equal, we conclude that both arcs have the same measure. This implies that JP bisects KM.
Two-Column Proof
Given: & ⊙ P, KM⊥JP
Prove: & JP bisectsKMandKM
Let's summarize the proof we did in the following two-column table.
