Question

Determine if triangle NOPNOP and triangle QRSQRS are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)

Answer 1

If the given triangles are similar then the following relation must be fulfilled:

`(QR)/(NO)=(RS)/(OP)=(SQ)/(PN)`

By substituting the given values, we have

`\begin{gathered} (QR)/(NO)=(75)/(15)=5 \\ \text{and} \\ (RS)/(OP)=(85)/(17)=5 \\ \text{and} \\ (SQ)/(PN)=(80)/(16)=5 \end{gathered}`

Since the 3 ratios are equal then both triangles are similar. Then, the answer is:

`\text{ The trianglea are similar because SSS. Thre}e\text{ sides proportionate}`