Question

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

Explanation:

Step1: Recall triangle - type definitions

An equilateral triangle has all sides equal. An isosceles triangle has at least two sides equal. A scalene triangle has all sides of different lengths.

Step2: Analyze Triangle A

The side - lengths of Triangle A are 4, 7, and 10. Since all side - lengths are different, it is a scalene triangle.

Step3: Analyze Triangle B

Triangle B has two angles equal to 45° and one right - angle. In a triangle, equal angles correspond to equal sides. So, it has two equal sides, making it an isosceles triangle.

Step4: Analyze Triangle C

The side - lengths of Triangle C are all 9. Since all sides are equal, it is an equilateral triangle. Also, since an equilateral triangle is a special case of an isosceles triangle, it is both equilateral and isosceles.

Step5: Analyze Triangle D

All angles of Triangle D are 60°. In a triangle, equal angles correspond to equal sides. So, all sides are equal, making it an equilateral triangle. And as an equilateral triangle is a special isosceles triangle, it is both equilateral and isosceles.

Answer:

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