We are given the following congruences.
∠ JKL&≅ ∠ MLK
∠ JLK&≅ ∠ MKL
Let's mark the congruent angles on the diagram and highlight the segments we are asked to compare.
We can see that triangles △ JKL and △ MLK have two pairs of congruent angles.
The side included between these angles is common and hence also congruent in the two triangles.
This means we can use the Angle-Side-Angle (ASA) Congruence Postulate to conclude that the two triangles are congruent.
△ JKL≅△ MLK
Let's summarize what we can see about the position of the highlighted segments.
Segment JK is opposite to angle ∠ JLK in triangle △ JKL.
Segment ML is opposite to angle ∠ MKL in triangle △ MLK.
Since these segments are opposite to corresponding congruent angles in the two triangles, these are corresponding segments.
We know that corresponding segments of congruent triangles are congruent, so we have proven the claim we were asked to prove.
JK≅ ML
