Question

are these triangles similar?
g
32°
h
57°
i
t
57°
32°
v
u
yes
no

Explanation:

Step1: Calculate missing angle in $\triangle GHI$

Sum of angles in triangle is $180^\circ$.
$\angle H = 180^\circ - 32^\circ - 57^\circ = 91^\circ$

Step2: Calculate missing angle in $\triangle TUV$

Sum of angles in triangle is $180^\circ$.
$\angle U = 180^\circ - 57^\circ - 32^\circ = 91^\circ$

Step3: Compare corresponding angles

$\angle G = \angle V = 32^\circ$, $\angle I = \angle T = 57^\circ$, $\angle H = \angle U = 91^\circ$. All corresponding angles are congruent, so triangles are similar by AA (Angle-Angle) similarity criterion.

Answer:

yes