Question

for each triangle, check all that apply. triangle a triangle b triangle c triangle d scalene isosceles equilateral scalene isosceles equilateral scalene isosceles equilateral scalene isosceles equilateral

Explanation:

Triangle A

Step1: Check side lengths

All sides are 9.

Step2: Check triangle type

Since all sides are equal, it is equilateral. Also, an equilateral triangle is a special case of isosceles (as it has at least two equal sides).

Triangle B

Step1: Check angles

All angles are \(60^{\circ}\).

Step2: Check triangle type

By the angle - side relationship (if all angles are equal, all sides are equal), it is equilateral. And as equilateral is a special isosceles, it is also isosceles.

Triangle C

Step1: Check side - angle relationships

No two sides are equal (since angles are \(90^{\circ},60^{\circ},30^{\circ}\) and in a triangle, larger angles have longer opposite sides).

Step2: Check triangle type

Since no sides are equal, it is scalene.

Triangle D

Step1: Check side lengths

Two sides are 6.

Step2: Check triangle type

Since at least two sides are equal, it is isosceles.

Answer:

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