Triangle Side Measurements: Determining if ABC is Equilateral

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

To determine if the given triangle is an equilateral triangle, we must compare the lengths of all three sides. An equilateral triangle requires all three sides to have the same length.

Given the side lengths:

• $AB = 7$
• $BC = 10$
• $CA = 9$

Step-by-step solution:

• Step 1: Compare $AB$ with $BC$. We see that $7 \neq 10$. Therefore, $AB \neq BC$.
• Step 2: Compare $AB$ with $CA$. We see that $7 \neq 9$. Therefore, $AB \neq CA$.
• Step 3: Since $AB \neq BC$ and $AB \neq CA$, the sides are not all equal.

Since the sides $AB$, $BC$, and $CA$ are not all equal, the triangle is not an equilateral triangle.

Thus, the solution to the problem is No.