Given ∠M = ∠N = 46°
It forms a pair of corresponding angles, hence LM || PN.
In ΔLMK and ΔPNK,
∠LMK = ∠PNK [corresponding angles]
∠MLK = ∠NPK [corresponding angles]
∠K = ∠K [common angle]
We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
∴ ΔLMK ~ ΔPNK
We know that two triangles are similar if their corresponding sides are proportional.
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