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:

1. Recall the definition of an isosceles triangle: A triangle with at least two congruent sides. By the Isosceles Triangle Theorem, if two sides of a triangle are congruent, then the angles opposite those sides (the base angles) are congruent. So, an isosceles triangle must have at least two congruent angles.
2. Analyze the other options:

• "All three angles are congruent" describes an equilateral triangle (a special case of isosceles, but not all isosceles triangles are equilateral).
• "The vertex angle is a right angle" is only true for isosceles right triangles, not all isosceles triangles.
• "The vertex angle is obtuse" is only true for isosceles triangles with an obtuse vertex angle, not all isosceles triangles.

Answer:

At least two of the angles are congruent.