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: Recall triangle types

• Scalene: All sides different.
• Isosceles: At least two sides equal.
• Equilateral: All three sides equal (also isosceles).

Triangle A has sides 9, 9, 9. All sides equal, so it's equilateral (and thus isosceles), not scalene.

Step2: Check each option

• Scalene: No (all sides equal).
• Isosceles: Yes (at least two sides equal, actually all three).
• Equilateral: Yes (all three sides equal).

Triangle B

Step1: Recall angle - side relations

In a triangle, equal angles correspond to equal sides. Triangle B has two angles of \(40^\circ\), so the sides opposite them are equal.

Step2: Check each option

• Scalene: No (two sides equal).
• Isosceles: Yes (two sides equal, from equal angles).
• Equilateral: No (angles are \(40^\circ, 40^\circ, 100^\circ\), not all \(60^\circ\), so sides not all equal).

Triangle C

Step1: Check side lengths

Triangle C has sides 7, 4, 10. All sides are different.

Step2: Check each option

• Scalene: Yes (all sides different).
• Isosceles: No (no two sides equal).
• Equilateral: No (all sides not equal).

Triangle D

Answer:

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

(To mark on the table:
Triangle A: Check Isosceles, Check Equilateral; Uncheck Scalene.
Triangle B: Check Isosceles; Uncheck Scalene, Uncheck Equilateral.
Triangle C: Check Scalene; Uncheck Isosceles, Uncheck Equilateral.
Triangle D: Check Scalene; Uncheck Isosceles, Uncheck Equilateral.)