In an isosceles triangle, which angles are congruent?

In an isosceles triangle, which angles are congruent?

• A. Angles opposite the equal sides
• B. The acute angles are equal
• C. The base angles are supplementary
• D. The vertex angle equals base angles

Answer: (A)

In an isosceles triangle, equal sides force the angles opposite those sides to be congruent. The two equal sides are the legs, and the angles opposite them are the base angles; those two angles must have the same measure. The vertex angle—between the two equal sides—generally differs from the base angles (only equal in the equilateral case). Also, the base angles don’t add up to 180 degrees by themselves; together with the vertex angle they sum to 180 degrees. So the correct statement is that the angles opposite the equal sides are congruent.

In an isosceles triangle, equal sides force the angles opposite those sides to be congruent. The two equal sides are the legs, and the angles opposite them are the base angles; those two angles must have the same measure. The vertex angle—between the two equal sides—generally differs from the base angles (only equal in the equilateral case). Also, the base angles don’t add up to 180 degrees by themselves; together with the vertex angle they sum to 180 degrees. So the correct statement is that the angles opposite the equal sides are congruent.