Question

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

Explanation:

Step1: Check SSS similarity ratio

For SSS similarity, the ratios of corresponding sides should be equal.
Let's assume \(\triangle DEF\) and \(\triangle RST\).
\(\frac{DE}{RS}=\frac{49}{76}\approx0.645\), \(\frac{DF}{RT}=\frac{35}{42}=\frac{5}{6}\approx0.833\), \(\frac{EF}{ST}=\frac{70}{44}=\frac{35}{22}\approx1.591\)
Since \(\frac{49}{76}
eq\frac{35}{42}
eq\frac{70}{44}\), SSS is not valid.

Step2: Check SAS similarity

For SAS similarity, two sides should be in proportion and the included angle should be equal.
We don't have information about the included angles and the side - side ratios are not equal as shown above.

Step3: Check AA similarity

We have no information about the angles to use AA (angle - angle) similarity.

Answer:

none of the above; the triangles cannot be proven similar