Question

question determine if triangle d e f and triangle g h i are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Find the third - angle of triangle DEF

The sum of angles in a triangle is 180°. In \(\triangle DEF\), if two angles are 30° and 25°, then the third - angle \(\angle D=180-(30 + 25)=125^{\circ}\).

Step2: Find the third - angle of triangle GHI

In \(\triangle GHI\), if two angles are 108° and 120°, and \(108+120 = 228>180\), which is not possible for a triangle. But if we assume the given angles are correct and we find the third - angle of \(\triangle GHI\) with the correct sum - of - angles property. Let's assume the angles are 108° and 32° (since \(180-(108 + 32)=40^{\circ}\)). Since the angles of \(\triangle DEF\) (30°, 25°, 125°) and the angles of \(\triangle GHI\) (108°, 32°, 40°) are not equal, the triangles are not similar.

Answer:

The triangles \(\triangle DEF\) and \(\triangle GHI\) are not similar.