If a triangle is isosceles, what can be said about its base angles?

If a triangle is isosceles, what can be said about its base angles?

• A. They are supplementary.
• B. They are equal.
• C. They are opposite the vertex angle.
• D. They are always obtuse.

Answer: (B)

In an isosceles triangle, the two sides that are equal are called the legs, and the angles at the ends of the base are the base angles. The key fact is: equal sides imply equal angles opposite them. Since the two equal sides are opposite the base angles, those base angles must be equal to each other. So, the base angles have the same measure, though they can be acute, right, or obtuse depending on the vertex angle. Remember, the vertex angle plus the two base angles add up to 180 degrees, but the base angles themselves are equal, not supplementary to each other.

In an isosceles triangle, the two sides that are equal are called the legs, and the angles at the ends of the base are the base angles. The key fact is: equal sides imply equal angles opposite them. Since the two equal sides are opposite the base angles, those base angles must be equal to each other.

So, the base angles have the same measure, though they can be acute, right, or obtuse depending on the vertex angle. Remember, the vertex angle plus the two base angles add up to 180 degrees, but the base angles themselves are equal, not supplementary to each other.