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:

Step1: Recall equilateral - triangle definition

An equilateral triangle has all three sides of equal length.

Step2: Analyze methods

The slope of the sides is related to the steepness and direction, not the side - length equality. To check if a triangle is equilateral, we need to check the side - length equality. The distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ is used to calculate the length of the sides. We should calculate the length of all three sides and check if they are congruent.

Answer:

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