Question

for each triangle, check all that apply

Explanation:

Step1: Recall triangle definitions

• Scalene triangle: All sides are of different lengths.
• Isosceles triangle: At least two sides are equal.
• Equilateral triangle: All three sides are equal.

Step2: Analyze Triangle A

• Angles are \(60^{\circ},60^{\circ},60^{\circ}\). By the angle - side relationship in triangles (if all angles are equal, all sides are equal). So it is an equilateral triangle (and since equilateral triangles are a special case of isosceles triangles, it is also isosceles).

Step3: Analyze Triangle B

• All angles (\(45^{\circ},75^{\circ},60^{\circ}\)) are different. By the angle - side relationship (different angles correspond to different side lengths), it is a scalene triangle.

Step4: Analyze Triangle C

• All sides are \(7\). So it is an equilateral triangle (and also isosceles).

Step5: Analyze Triangle D

• Two sides are \(8\). So it is an isosceles triangle.

Answer:

• Triangle A: Isosceles, Equilateral
• Triangle B: Scalene
• Triangle C: Isosceles, Equilateral
• Triangle D: Isosceles