Question

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

Explanation:

Step1: Recall similarity criterion

For two triangles to be similar, the ratios of corresponding sides must be equal and corresponding angles must be congruent. Here we check angle - angle (AA) similarity.

Step2: Analyze angles in triangles

In \(\triangle DEF\), two angles are \(49^{\circ}\). In \(\triangle GHI\), one angle is \(49^{\circ}\) and another is \(82^{\circ}\). The third - angle of \(\triangle DEF\) is \(180^{\circ}-49^{\circ}-49^{\circ}=82^{\circ}\) (since the sum of angles in a triangle is \(180^{\circ}\)). So, \(\triangle DEF\) has angles \(49^{\circ},49^{\circ},82^{\circ}\) and \(\triangle GHI\) has angles \(49^{\circ},82^{\circ},49^{\circ}\).

Step3: Apply AA similarity

Since the corresponding angles of \(\triangle DEF\) and \(\triangle GHI\) are congruent, by the AA (angle - angle) similarity criterion, the two triangles are similar.

Answer:

The triangles are similar.