DESCRIBE IN WORDS what you would calculate and how you would determine whether the triangle with vertices A (2,1), B (5,3), and C (0,4) is isosceles, equilateral, or scalene. Do NOT do the calculations!
To determine whether the triangle with vertices A (2,1), B (5,3), and C (0,4) is isosceles, equilateral, or scalene, I would calculate the lengths of all three sides of the triangle. Based on the lengths obtained, I would compare them to each other.
If all three sides have the same length, then the triangle would be equilateral. This means that all three vertices are equidistant from each other.
If only two sides have the same length, while the third side has a different length, then the triangle would be isosceles. This means that two vertices are equidistant from each other, but the third one is not.
If all three sides have different lengths, then the triangle would be scalene. This means that no two vertices are equidistant from each other.
To determine whether the triangle with vertices A (2,1), B (5,3), and C (0,4) is isosceles, equilateral, or scalene without performing any calculations, we can analyze the lengths of the sides of the triangle.
First, we need to find the distance between the points A and B, B and C, and C and A. This can be done using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is calculated as the square root of ((x2 - x1)^2 + (y2 - y1)^2).
Once we have the distances between the points, we compare them. If all three distances are equal, then the triangle is equilateral. If two sides are equal, but the third side is different, then the triangle is isosceles. Lastly, if all three sides have different lengths, then the triangle is scalene.
Therefore, by comparing the distances between the vertices of the given triangle, we can determine whether it is isosceles, equilateral, or scalene without actually performing the calculations.