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 logi select choice its (1) and (2).

Explanation:

• Statement (1): Defines an equilateral triangle as having three congruent sides.
• Statement (2): Tells that if all sides of a triangle are congruent (equilateral), each angle is \(60^{\circ}\).
• Option A: A non - equilateral triangle (like an isosceles triangle with angles \(70^{\circ},70^{\circ},40^{\circ}\)) can have congruent angles. But this is not directly related to the logical flow from (1) and (2) about equilateral triangles.
• Option B: A figure with three congruent sides is an equilateral triangle by definition (matches statement (1)).
• Option C: A non - equilateral triangle can have an angle of \(60^{\circ}\) (e.g., a triangle with angles \(60^{\circ}, 80^{\circ},40^{\circ}\)). And it does not follow from statements (1) and (2) which are about equilateral triangles.
• Option D: If a triangle is equilateral (from (1) it has three congruent sides), then from (2) each angle is \(60^{\circ}\).

Answer:

Statement \(C\) does not belong. Statement \(D\) follows logically from statements (1) and (2). Statements \(A\) and \(C\) do not follow logically from (1) and (2) (statement \(B\) is just a re - statement of (1) in a different form).