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 equal - length sides. By the Isosceles Triangle Theorem, the angles opposite the equal - length sides (the base angles) are congruent. So, an isosceles triangle has at least two congruent angles.
2. Analyze the other options:

• Option "All three angles are congruent": A triangle with all three angles congruent is an equilateral triangle. While an equilateral triangle is a special case of an isosceles triangle, not all isosceles triangles are equilateral. So, this statement is not always true for isosceles triangles.
• Option "The vertex angle is a right angle": An isosceles triangle can have an acute, right, or obtuse vertex angle. For example, an isosceles triangle with two sides of length 3 and a base of length 2 has an acute vertex angle. So, the vertex angle is not always a right angle.
• Option "The vertex angle is obtuse": An isosceles triangle can have an acute vertex angle (e.g., an isosceles triangle with two sides of length 5 and a base of length 6). So, the vertex angle is not always obtuse.

Answer:

B. At least two of the angles are congruent.