Question

which rule explains why these scalene triangles are similar?

options:
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Identify included sides/angle

We have two triangles with one pair of equal included angles (the marked angles at S and I). The sides forming these angles are:
For $\triangle SRT$: $SS = 56$, $SR = 72$
For $\triangle IJK$: $SI = 65$, $IJ = 62$

Step2: Calculate side ratios

Compute the ratio of corresponding sides:
$\frac{SS}{SI} = \frac{56}{65} \approx 0.8615$
$\frac{SR}{IJ} = \frac{72}{62} \approx 1.1613$

Step3: Compare ratios for SAS similarity

For SAS similarity, the ratios of the two pairs of corresponding sides forming the equal included angle must be equal. Since $\frac{56}{65}
eq \frac{72}{62}$, SAS does not apply. We have no information about other angles or the third pair of sides, so SSS and AA also do not apply.

Answer:

none of the above; the triangles cannot be proven similar