Question

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

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(QRP\) and \(WUV\), we have:

• \(\frac{QR}{WU}=\frac{75}{44}\approx1.7045\)
• \(\frac{RP}{WV}=\frac{66}{38}\approx1.7368\)
• \(\frac{QP}{UV}=\frac{57}{50} = 1.14\)

Since \(\frac{75}{44}
eq\frac{66}{38}
eq\frac{57}{50}\), the \(SSS\) (Side - Side - Side) similarity rule (which requires \(\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}\)) does not apply.

There is no information about included angles to check the \(SAS\) (Side - Angle - Side) similarity rule (which requires \(\frac{a}{a'}=\frac{b}{b'}\) and the included angles equal).

There is no information about two pairs of equal angles to check the \(AA\) (Angle - Angle) similarity rule.

Answer:

none of the above; the triangles cannot be proven similar