Question

what is always true about the angles of an isosceles triangle?

all three angles are congruent.
at least two of the angles are congruent.
the vertex angle is a right angle.
the vertex angle is obtuse.

Explanation:

Define an isosceles triangle

An isosceles triangle is defined as a triangle with at least two congruent sides.

Apply the Isosceles Triangle Theorem

By the Isosceles Triangle Theorem, the angles opposite the congruent sides are also congruent. Therefore, an isosceles triangle must have at least two congruent angles.

Evaluate the given options

• "All three angles are congruent" is only true for equilateral triangles.
• "At least two of the angles are congruent" is always true by definition and theorem.
• "The vertex angle is a right angle" is only true for right isosceles triangles.
• "The vertex angle is obtuse" is only true for obtuse isosceles triangles.

Answer:

• All three angles are congruent.
• At least two of the angles are congruent. (Correct answer)
• The vertex angle is a right angle.
• The vertex angle is obtuse.