Question

1. what is the minimum number of angles that must be shown to be congruent to prove that 2 triangles are similar, and why? a. zero because the angles of similar triangles are not congruent b. one because if 1 pair of angles is congruent, then the remaining pairs are congruent c. two because if 2 pairs of angles are congruent, then the third pair is also congruent d. three because similar triangles have 3 pairs of congruent angles

Explanation:

The sum of the interior angles of a triangle is \(180^{\circ}\). If two pairs of angles in two triangles are congruent, then the third pair of angles must also be congruent (since \(180^{\circ}-\text{(sum of two congruent angles)} = 180^{\circ}-\text{(sum of two congruent angles)}\)). The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Answer:

C. two because if 2 pairs of angles are congruent, then the third pair is also congruent