Question

for each triangle, check all that apply.

triangle a (sides 12, 12, 12)	triangle b (sides 7, 6, 5)	triangle c (sides 10, 10, 14)

Explanation:

Step1: Analyze Triangle A

Triangle A has sides 12, 12, 12. An equilateral triangle has all sides equal, and an isosceles triangle has at least two equal sides. Since all three sides are equal, Triangle A is equilateral (and also isosceles, but equilateral is more specific here). It is not scalene (scalene has all sides different).

Step2: Analyze Triangle B

Triangle B has sides 5, 6, 7. All sides are of different lengths. A scalene triangle has all sides different, so Triangle B is scalene. It is not isosceles (no two sides equal) or equilateral (all sides equal).

Step3: Analyze Triangle C

Triangle C has sides 10, 10, 14. Two sides are equal (10 and 10), so it is isosceles. It is not scalene (has two equal sides) or equilateral (all sides not equal).

Answer:

• Triangle A: $\boxed{\text{Isosceles}}$, $\boxed{\text{Equilateral}}$ (but since equilateral is a type of isosceles, and the options are checkboxes, we check Isosceles and Equilateral)
• Triangle B: $\boxed{\text{Scalene}}$
• Triangle C: $\boxed{\text{Isosceles}}$

(Note: In the original problem's checkbox format, for Triangle A, we check "Isosceles" and "Equilateral"; for Triangle B, check "Scalene"; for Triangle C, check "Isosceles".)