Question

determine if triangle fgh and triangle ijk 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: Find missing angle in $\triangle FGH$

Sum of angles in triangle is $180^\circ$.
$\angle G = 180^\circ - 54^\circ - 38^\circ = 88^\circ$

Step2: Find missing angle in $\triangle IJK$

Sum of angles in triangle is $180^\circ$.
$\angle J = 180^\circ - 54^\circ - 38^\circ = 88^\circ$

Step3: Match corresponding angles

In $\triangle FGH$: $\angle H=54^\circ$, $\angle F=38^\circ$, $\angle G=88^\circ$
In $\triangle IJK$: $\angle K=54^\circ$, $\angle I=38^\circ$, $\angle J=88^\circ$
All corresponding angles are equal.

Answer:

The triangles are similar, by the AA (Angle-Angle) similarity criterion (all three corresponding angles are equal, satisfying the condition for similarity).