Question

1. two triangles share a 90° angle and a 45° angle. what can be said about the triangles? a. they are proportional but not similar. b. they are congruent. c. they are not similar. d. they are similar by the aa criterion.

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Step2: Analyze the given angles

One angle is \(90^{\circ}\) and another is \(45^{\circ}\). For a triangle, the sum of angles is \(180^{\circ}\). So the third angle in each triangle is \(180-(90 + 45)=45^{\circ}\). So both triangles have angles \(90^{\circ},45^{\circ},45^{\circ}\).

Answer:

d. They are similar by the AA criterion.