The triangles are not similar because their corresponding angles are not congruent to each other.
How to Determine if Two Triangles are Similar?
If two triangles are similar, their corresponding angles will be congruent to each other. Therefore, two triangles with congruent angles are either similar or congruent to each other. If they are similar, their corresponding sides will have proportional length.
From the image given, the angles of triangle ABC are:
C = 30
B = 90
A = 180 - 90 - 30 = 60.
Triangle LMN are:
L = 90
M = 55
N = 180 - 55 - 90 = 35
Thus, the corresponding angles are not congruent, therefore, they are not similar.
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