Question

which pair of triangles are similar?

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if their corresponding angles are equal. The sum of angles in a triangle is 180°.

Step2: Analyze first - pair

For the first pair of triangles:
In the first triangle, angles are 20° and 120°. The third angle is \(180-(20 + 120)=40^{\circ}\). In the second triangle, angles are 20° and 40°. The third angle is \(180-(20 + 40)=120^{\circ}\). The corresponding angles of the two triangles are equal (20° - 20°, 40° - 40°, 120° - 120°).

Step3: Analyze second - pair

In the second - pair, the angles are 70°, 30° and 75°, 20°. Since \(70
eq75\), \(30
eq20\), they are not similar.

Step4: Analyze third - pair

In the third - pair, one triangle has angles 45°, 90° and the other has angles 60°, 90°. Since \(45
eq60\), they are not similar.

Step5: Analyze fourth - pair

In the fourth - pair, the angles are 50°, 50° and 60°, 60°. Since \(50
eq60\), they are not similar.

Answer:

The first pair of triangles are similar.