Question

question
determine if triangle jkl and triangle mno are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles
similar.

Explanation:

Step1: Find the third angle of triangle \(MNO\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle MNO\), if two angles are \(41^{\circ}\) and \(76^{\circ}\), then the third angle \(\angle M=180-(41 + 76)=63^{\circ}\).

Step2: Check the ratios of corresponding sides

For \(\triangle JKL\) with sides \(JK = 10\), \(KL=14\) and \(\triangle MNO\) with sides \(NO = 70\), \(MN = 50\).
The ratio of \(JK\) to \(MN\) is \(\frac{JK}{MN}=\frac{10}{50}=\frac{1}{5}\).
The ratio of \(KL\) to \(NO\) is \(\frac{KL}{NO}=\frac{14}{70}=\frac{1}{5}\).

Step3: Check the equality of corresponding angles

\(\angle K=\angle N = 76^{\circ}\).
Since the ratios of two pairs of corresponding sides are equal (\(\frac{JK}{MN}=\frac{KL}{NO}=\frac{1}{5}\)) and the included angles (\(\angle K\) and \(\angle N\)) are equal, by the Side - Angle - Side (SAS) similarity criterion.

Answer:

The triangles \(JKL\) and \(MNO\) are similar.