Question

which rule explains why these triangles are similar?
options:
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Calculate side ratios

$\frac{IG}{ST} = \frac{42}{51} = \frac{14}{17}$, $\frac{GH}{RS} = \frac{54}{60} = \frac{9}{10}$, $\frac{HI}{TR} = \frac{66}{80} = \frac{33}{40}$

Step2: Check ratio equality

$\frac{14}{17}
eq \frac{9}{10}
eq \frac{33}{40}$, so SSS fails.

Step3: Check SAS/AA conditions

No angle measures provided to verify SAS (2 sides + included angle) or AA (2 matching angles).

Answer:

none of the above; the triangles cannot be proven similar