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 select choice does not belong. statement select choice follows logically from statements (1) and (2). statements select choice do not follow logi ts (1) and (2).

Explanation:

Step1: Analyze statement A

Statement (1) is about an equilateral triangle having three congruent sides. Statement (2) is about a triangle with all - congruent sides having \(60^{\circ}\) angles. An isosceles triangle (not equilateral) can have congruent angles (e.g., an isosceles right - triangle has two \(45^{\circ}\) angles). So, statement A is false.

Step2: Analyze statement B

If a figure has three congruent sides, by the definition of an equilateral triangle (a triangle with three congruent sides), it is an equilateral triangle. This follows from the basic definition related to the statements (1) (which is about triangle properties).

Step3: Analyze statement C

A non - equilateral triangle can have a \(60^{\circ}\) angle. For example, a triangle with angles \(60^{\circ}, 70^{\circ}, 50^{\circ}\). So, statement C is false.

Step4: Analyze statement D

If a triangle is equilateral (from statement (1) it has three congruent sides), and from statement (2) a triangle with all congruent sides has each angle equal to \(60^{\circ}\). So, statement D follows logically.

Answer:

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