Question

ava claims the following two statements. (1) \every equilateral triangle should be classified as an acute isosceles triangle.\ (2) \every acute isosceles triangle is an equilateral triangle.\ using \isosceles = at least two congruent sides,\ which statement best evaluates her claim?

both statements are true.

both statements are false.

the first statement is false and the second is true.

the first statement is true and the second is false.

Explanation:

Step1: Analyze statement (1)

An equilateral triangle has all three sides equal (so it has at least two congruent sides, making it isosceles) and all angles equal to \(60^{\circ}\) (acute, since \(60^{\circ}<90^{\circ}\)). So, "Every equilateral triangle should be classified as an acute isosceles triangle" is true.

Step2: Analyze statement (2)

An acute isosceles triangle has two congruent sides and all angles less than \(90^{\circ}\). For example, a triangle with angles \(80^{\circ},80^{\circ},20^{\circ}\) is acute isosceles but not equilateral (since not all sides are equal). So, "Every acute isosceles triangle is an equilateral triangle" is false.

Answer:

The first statement is true and the second is false.