Question

question
determine if triangle klm and triangle nop are or are not similar, and, if they are, state how you know.
(note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles similar

Explanation:

Step1: Calculate ∠M in △KLM

Sum of angles in a triangle is $180^\circ$.
$\angle M = 180^\circ - 53^\circ - 83^\circ = 44^\circ$

Step2: Calculate ∠P in △NOP

Sum of angles in a triangle is $180^\circ$.
$\angle P = 180^\circ - 53^\circ - 83^\circ = 44^\circ$

Step3: Compare corresponding angles

In △KLM: $\angle K=53^\circ$, $\angle L=83^\circ$, $\angle M=44^\circ$
In △NOP: $\angle N=53^\circ$, $\angle O=83^\circ$, $\angle P=44^\circ$
All corresponding angles are equal.

Answer:

The triangles are similar by the AA (Angle-Angle) similarity criterion, as all corresponding interior angles of the two triangles are equal.