Question

1. which triangles are similar to triangle a? a) both b) b c) c d) none 6. are the triangles similar? a) yes b) no 7. are the triangles similar? a) yes b) no

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 triangle A in question 5

In triangle A, the third - angle is \(180-(58 + 54)=68^{\circ}\). In triangle B, the angles are 54° and 68°, and its third - angle is \(180-(54 + 68)=58^{\circ}\). Since the angles of triangle A and triangle B are equal, they are similar. Triangle C has angles 47° and 51°, and its third - angle is \(180-(47 + 51)=82^{\circ}\), so it is not similar to triangle A.

Step3: Analyze question 6

In triangle ABC, the third - angle is \(180-(60 + 81)=39^{\circ}\). In triangle DEF, the third - angle is \(180-(40 + 81)=59^{\circ}\). Since the corresponding angles are not equal, the triangles are not similar.

Step4: Analyze question 7

In triangle ABC, \(\angle A=180-(90 + 35)=55^{\circ}\), \(\angle C = 90^{\circ}\), \(\angle B=35^{\circ}\). In triangle DEF, \(\angle D = 55^{\circ}\), \(\angle F=90^{\circ}\), \(\angle E=35^{\circ}\). Since the corresponding angles are equal, the triangles are similar.

Answer:

1. b) B
2. b) No
3. a) Yes