Question

are these triangles similar?
triangle hfg with sides: hf=45, fg=35, hg=60. triangle rst with sides: rs=54, st=42, rt=72.
options: yes, no

Explanation:

Step1: Order the sides of each triangle

For triangle \( FHG \) (sides: 35, 45, 60), order them: 35, 45, 60.
For triangle \( STR \) (sides: 42, 54, 72), order them: 42, 54, 72.

Step2: Check the ratios of corresponding sides

Calculate the ratios:
\( \frac{35}{42} = \frac{5}{6} \),
\( \frac{45}{54} = \frac{5}{6} \),
\( \frac{60}{72} = \frac{5}{6} \).

Since all three ratios are equal, the triangles are similar by the SSS (Side - Side - Side) similarity criterion.

Answer:

yes