Question

mary thinks the triangle is equilateral. how would you support or dispute her conjecture?
calculate the slope of all three sides, and check whether the slopes are equal.
calculate the slope of all three sides, and check whether any slopes are reciprocals.
use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
use the distance formula to calculate the length of all three sides, and check whether any two sides are congruent.

Explanation:

An equilateral triangle has all three sides congruent (equal in length). Slope is related to the steepness of a line (angle), not side length, so options about slope (first two) are irrelevant for checking side congruence. The fourth option checks for at least two congruent sides (isosceles or equilateral), but to confirm equilateral, we need all three sides congruent. The third option uses the distance formula to calculate all three side lengths and checks if they are equal, which is the correct method to verify an equilateral triangle.

Answer:

C. Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.