Question

decide whether the triangles are similar. if they are, write a similarity statement and state the reason justifying the similarity.
if necessary, you may learn what the markings on a figure indicate.

1.
not similar or not necessarily similar
similar:
$\triangle xyz \sim \triangle nmy$ by the
angle-angle (aa) similarity property

2.
not similar or not necessarily similar
similar:
$\triangle abc \sim \square$ by the
select

3.
not similar or not necessarily similar
similar:
$\triangle jkl \sim \square$ by the
select

Explanation:

Step1: Analyze first triangle pair

$\angle NYM = \angle ZYX$ (vertical angles, equal). $\angle N = \angle Z$ (right angles, equal). By AA Similarity, $\triangle XYZ \sim \triangle NMY$ (matches given selection).

Step2: Analyze second triangle pair

Calculate side ratios:
$\frac{AB}{DE} = \frac{6}{4} = 1.5$, $\frac{BC}{DF} = \frac{7}{5} = 1.4$, $\frac{AC}{EF} = \frac{8}{6} \approx 1.33$.
Ratios are not equal, so no similarity.

Step3: Analyze third triangle pair

Find missing angle in $\triangle IGH$:
$\angle I = 180^\circ - 110^\circ - 50^\circ = 20^\circ$.
In $\triangle JKL$, $\angle J = 180^\circ - 50^\circ - 20^\circ = 110^\circ$.
$\angle L = \angle H = 50^\circ$, $\angle J = \angle G = 110^\circ$. By AA Similarity, $\triangle JKL \sim \triangle HGI$.

Answer:

1. $\triangle XYZ \sim \triangle NMY$ by the Angle-Angle (AA) Similarity Property (correct as selected)
2. Not similar or not necessarily similar
3. $\triangle JKL \sim \triangle HGI$ by the Angle-Angle (AA) Similarity Property