Question

lesson 4 - 2: exit ticket
which of the following statements is incorrect?
a triangle with three congruent sides is equiangular.
the isosceles triangle theorem can be applied to equilateral triangles.
the measure of each angle of an equilateral triangle is 120°.
a triangle with three congruent angles is equilateral.

Explanation:

Step1: Recall properties of equilateral triangles

An equilateral triangle has three congruent sides and three congruent angles. The sum of the interior angles of a triangle is \(180^{\circ}\). If all three angles are congruent, then each angle \(=\frac{180^{\circ}}{3}=60^{\circ}\).

Step2: Analyze each statement

• Statement 1: A triangle with three congruent sides (equilateral) has three congruent angles (equiangular). This is correct.
• Statement 2: An equilateral triangle is a special case of an isosceles triangle (where at least two sides are equal). So, the Isosceles Triangle Theorem (if two sides of a triangle are congruent, then the angles opposite those sides are congruent) can be applied. This is correct.
• Statement 3: Since the sum of angles in a triangle is \(180^{\circ}\), for an equilateral triangle, each angle \(=\frac{180^{\circ}}{3} = 60^{\circ}

eq120^{\circ}\). This is incorrect.

• Statement 4: A triangle with three congruent angles (each \(60^{\circ}\)) has three congruent sides (equilateral). This is correct (by the converse of the Isosceles Triangle Theorem extended for three angles).

Answer:

The measure of each angle of an equilateral triangle is \(120^{\circ}\)