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.) answer attempt 2 out of 2 the triangles similar.

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if two - pairs of corresponding angles are equal.

Step2: Identify angles in \(\triangle DEF\)

In \(\triangle DEF\), \(\angle D = 49^{\circ}\), \(\angle F=49^{\circ}\), and \(\angle E=180^{\circ}-49^{\circ}-49^{\circ}=82^{\circ}\) (using the angle - sum property of a triangle: \(\angle A+\angle B+\angle C = 180^{\circ}\)).

Step3: Identify angles in \(\triangle GHI\)

In \(\triangle GHI\), \(\angle H = 82^{\circ}\), \(\angle I = 49^{\circ}\), and \(\angle G=180^{\circ}-82^{\circ}-49^{\circ}=49^{\circ}\) (using the angle - sum property of a triangle).

Step4: Compare angles

We have \(\angle D=\angle I = 49^{\circ}\), \(\angle E=\angle H = 82^{\circ}\), and \(\angle F=\angle G = 49^{\circ}\). Since two pairs of corresponding angles are equal (in fact, all three pairs are equal), by the AA (angle - angle) similarity criterion, the two triangles are similar.

Answer:

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