Question

question determine if triangle nop and triangle qrs are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Check the ratio of corresponding sides

For triangle \(NOP\) and \(QRS\), we consider the sides adjacent to the \(58^{\circ}\) angle.
The ratio of \(NO = 16\) to \(QS=125\) is \(\frac{16}{125}\), and the ratio of \(NP = 27\) to \(QR = 80\) is \(\frac{27}{80}\).
Since \(\frac{16}{125}
eq\frac{27}{80}\) (because \(16\times80=1280\) and \(27\times125 = 3375\)).

Step2: Use the Side - Angle - Side (SAS) similarity criterion

The SAS similarity criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar. Here, the included angles (\(58^{\circ}\)) are equal, but the ratios of the adjacent sides are not equal.

Answer:

Triangle \(NOP\) and triangle \(QRS\) are not similar.