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:

Step1: Recall the definition of an isosceles triangle

An isosceles triangle has at least two congruent sides.

Step2: Use the property of angles opposite congruent sides

By the Isosceles Triangle Theorem, the angles opposite the congruent sides are congruent. So, an isosceles triangle has at least two congruent angles.

Step3: Analyze other options

• All three angles are congruent: This is true for an equilateral triangle (a special case of isosceles), but not all isosceles triangles.
• The vertex angle is a right angle: Only in a right - isosceles triangle.
• The vertex angle is obtuse: Not always. It can be acute or right - angled in some cases.

Answer:

At least two of the angles are congruent.