Question

for each triangle, check all that apply.
triangle a\ttriangle b\ttriangle c\ttriangle d
(figure of triangle a with side lengths 6, 6, 10)\t(figure of triangle b with angles 40°, 40°, 100°)\t(figure of triangle c with side lengths 7, 5, 11)\t(figure of triangle d with angles 60°, 60°, 60°)
☐ scalene\t☐ scalene\t☐ scalene\t☐ scalene
☐ isosceles\t☐ isosceles\t☐ isosceles\t☐ isosceles
☐ equilateral\t☐ equilateral\t☐ equilateral\t☐ equilateral

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 and all angles are \(60^{\circ}\).

Step2: Analyze Triangle A

Two sides are \(6\) (equal), so it is isosceles.

Step3: Analyze Triangle B

Two angles are \(40^{\circ}\), so the sides opposite these angles are equal (by the converse of the base - angles theorem in isosceles triangles). So it is isosceles.

Step4: Analyze Triangle C

All sides (\(5\), \(7\), \(11\)) are of different lengths. So it is scalene.

Step5: Analyze Triangle D

All angles are \(60^{\circ}\), so all sides are equal (equilateral triangle property). Also, since an equilateral triangle is a special case of an isosceles triangle (where at least two sides are equal), it is both isosceles and equilateral.

Answer:

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