Question

How can you prove a triangle is an equilateral triangle? (4 points)

a
Use the distance formula to see if at least two sides are congruent.

b
Use the slope formula to see if any sides are perpendicular.

c
Use the distance formula to see if all three sides are congruent.

d
Use the slope formula to see if any sides are parallel.

Answer 1

Answer:

A would be correct.

Step-by-step explanation:

Just show that triangles AOB,BOC,COA are all congruent (then all the sides of triangle ABC must be equal). To show this, note that triangles A′BO,A′OC are equilateral since they are all radius of the circles. Line OA′ is perpendicular to line BC. Hence, ∠OBC=∠OCB=30∘.

Answer 2

Answer:c

Use the distance formula to see if all three sides are congruent.

Step-by-step explanation:

An equilateral triangle is a triangle which has three sides with the same lengths. If we check for congruence we are checking to see if all the sides are the same :)