Question

1. are the triangles similar? a) yes b) no 4. which triangles are similar to triangle a? a) b b) none c) c d) both

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if their corresponding angles are equal.

Step2: Analyze angles of first - pair of triangles

In \(\triangle PIT\), angles are \(100^{\circ}\) and \(30^{\circ}\), so the third angle is \(180-(100 + 30)=50^{\circ}\). In \(\triangle BET\), angles are \(100^{\circ}\) and \(45^{\circ}\), so the third angle is \(180-(100 + 45)=35^{\circ}\). Since the corresponding angles are not equal, the triangles are not similar.

Step3: Analyze angles of second - set of triangles

In \(\triangle A\), angles are \(57^{\circ}\) and \(44^{\circ}\), third angle is \(180-(57 + 44)=79^{\circ}\). In \(\triangle B\), angles are \(79^{\circ}\) and \(44^{\circ}\), third angle is \(180-(79 + 44)=57^{\circ}\). In \(\triangle C\), angles are \(57^{\circ}\) and \(44^{\circ}\), third angle is \(180-(57+44)=79^{\circ}\). Triangles \(A\), \(B\) and \(C\) have the same set of angles, so they are similar.

Answer:

1. b) No
2. d) Both