Determine whether the conjecture is true or false. Give a counterexample if the conjecture is false

line-segment

#1

Determine whether the conjecture is true or false. Give a counterexample if the conjecture is false. Given: line segment AB,BC, and AC are congruent.
Conjecture: A, B, and C are collinear.

Answer:

False. If line segments AB, BC and AC are congruent, then ABC would be an equilateral triangle.

To be collinear, points A, B and C would have to lie on the same line. This is impossible as the line segments make up a triangle.