Question

determine if triangle opq and triangle rst, 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 3
the triangles are similar because
sss: three sides proportionate
sss: three sides congruent
sas: two sides proportionate, included angle congruent
sas: two sides + included angle congruent
aa: two angles congruent

Explanation:

Step1: Identify side lengths

For triangle \( OPQ \): sides are \( OQ = 18 \), \( PQ = 18 \), \( OP = 27 \).
For triangle \( RST \): sides are \( ST = 54 \), \( RS = 81 \), \( RT = 54 \).

Step2: Check side proportions

Calculate ratios of corresponding sides:
\( \frac{OQ}{RT} = \frac{18}{54} = \frac{1}{3} \),
\( \frac{PQ}{ST} = \frac{18}{54} = \frac{1}{3} \),
\( \frac{OP}{RS} = \frac{27}{81} = \frac{1}{3} \).

All three sides are proportional (ratio \( \frac{1}{3} \)). By SSS (Side - Side - Side) similarity criterion (three sides proportionate), the triangles are similar.

Answer:

The triangles are similar because SSS: three sides proportionate.