Question

1. which of the following statements identifies and explains whether the two triangles are similar? the triangles are similar because there are at least two pairs of congruent angles. the triangles are similar because each triangle has a 52° angle. the triangles are not similar because the triangles are different sizes. the triangles are not similar because the variables x and y have different values.

Explanation:

Step1: Recall similarity criterion

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

Step2: Analyze given angles

In the first triangle, angles are \(24^{\circ}\), \(52^{\circ}\), and \(x\). Using the angle - sum property of a triangle (\(x = 180-(24 + 52)=104^{\circ}\)). In the second triangle, angles are \(52^{\circ}\), \(104^{\circ}\), and \(y\). Using the angle - sum property of a triangle (\(y=180-(104 + 52)=24^{\circ}\)).

Step3: Determine similarity

Since the two triangles have two pairs of congruent angles (\(24^{\circ}\) and \(52^{\circ}\)), they are similar.

Answer:

The triangles are similar because there are at least two pairs of congruent angles.