Question

which one doesnt belong? use statements (1) and (2). determine which statement does not belong. justify your conclusion.
(1) if a triangle is equilateral, then it has three congruent sides.
(2) if all the sides of a triangle are congruent, then each angle measures 60°.
a if a triangle is not equilateral, then it cannot have congruent angles.
b a figure with three congruent sides is always an equilateral triangle.
c if a triangle is not equilateral, then none of the angles measures 60°.
d if a triangle is equilateral, then each of its angles measures 60°.
statement c does not belong. statement d follows logically from statements (1) and (2). statements a, b, and c do not follow logically from statements (1) and (2).

Explanation:

• Analyze each statement:
• Statement (1) defines an equilateral triangle as having three congruent sides.
• Statement (2) says if all sides of a triangle are congruent (equilateral), each angle is \(60^{\circ}\).
• Statement A: A non - equilateral triangle (e.g., isosceles) can have congruent angles. So it doesn't follow.
• Statement B: A figure with three congruent sides is an equilateral triangle by definition (from statement (1)), so it follows.
• Statement C: A non - equilateral triangle (e.g., a triangle with angles \(60^{\circ},60^{\circ},60^{\circ}\) is equilateral, but a triangle with angles \(60^{\circ}, 60^{\circ}, 60^{\circ}\) is equilateral. A non - equilateral triangle can have a \(60^{\circ}\) angle (e.g., a triangle with angles \(60^{\circ}, 70^{\circ}, 50^{\circ}\)). So it doesn't follow.
• Statement D: Directly follows from statement (2).

Answer:

Statement \(A\) and \(C\) do not belong. Statement \(D\) follows logically from statements (1) and (2).