Are the triangles similar? Yes. Similarity statement: △ JPK~△ JML Explanation: See solution.
Practice makes perfect
Let's notice that △ JPK and △ JML have one corresponding congruent angle, as ∠ J≅ ∠ J by the Reflexive Property. Since we have no information about the side lengths, let's think how we can prove similarity using angle measures.
Now recall the Corresponding Angles Postulate.
If parallel lines are cut by a transversal,
then the pairs of corresponding angles
are congruent.
Since we know that KP is parallel to LM, then ∠ JPK and ∠ JML are congruent angles, just as ∠ JKP and ∠ JLM.
As we can see, these two triangles have congruent corresponding angles. Therefore, by the Angle-Angle Similarity Theorem, △ JPK and △ JML are similar.
