Question

△jkl and △mno are shown below. which statement is true? △jkl is similar to △mno. △jkl is not similar to △mno. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate the third angle of \(\triangle JKL\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle JKL\), if two angles are \(27^{\circ}\) and \(37^{\circ}\), then the third angle \( \angle K=180^{\circ}-(27^{\circ} + 37^{\circ})=116^{\circ}\).

Step2: Calculate the third angle of \(\triangle MNO\)

For \(\triangle MNO\), if two angles are \(27^{\circ}\) and \(126^{\circ}\), then the third angle \( \angle O=180^{\circ}-(27^{\circ}+126^{\circ}) = 27^{\circ}\).
Since the angles of \(\triangle JKL\) (\(27^{\circ},37^{\circ},116^{\circ}\)) and \(\triangle MNO\) (\(27^{\circ},27^{\circ},126^{\circ}\)) are not equal in proportion (i.e., there is no correspondence of angles such that \(\angle J=\angle M\), \(\angle K=\angle N\), \(\angle L=\angle O\) or any other valid angle - correspondence for similarity), the triangles are not similar.

Answer:

\(\triangle JKL\) is not similar to \(\triangle MNO\).