One of the best ways to prove whether a statement is true or false is to assume it as true until we come up with a counterexample. Let's try assuming it's true. That statement translates to saying that if a triangle's corresponding angles are the same measures, its corresponding angles and its corresponding sides must be equal in measure. If that's true, all equilateral triangles must be congruent (because every angle in an equilateral triangle is 60°). Another way of saying that is: All equilateral triangles must have the same size. Is that true? Of course not! An equilateral triangle could have sides of 6 inches or 6 miles, and its angles would still be 60°. That means the statement is false. |