In the Isosceles Triangle Theorem, which angles are congruent?

In the Isosceles Triangle Theorem, which angles are congruent?

• A. Angles opposite the equal sides are congruent
• B. The base angles are supplementary
• C. The medians are perpendicular
• D. All sides are equal

Answer: (A)

In an isosceles triangle, the equal sides create a symmetry that forces the angles opposite those sides to be the same. So the angles opposite the equal sides are congruent. If two sides, say AB and AC, are equal, then the angles at B and C are congruent—the base angles. That’s exactly what the Isosceles Triangle Theorem states, and it explains why those two base angles are equal, no matter how the triangle is drawn as long as two sides are equal. The other ideas—base angles being supplementary, medians always perpendicular, or all sides being equal—do not describe this theorem: equilateral (all sides equal) is a different case, and the base angles being supplementary or medians always perpendicular aren’t general consequences of two sides being equal.

In an isosceles triangle, the equal sides create a symmetry that forces the angles opposite those sides to be the same. So the angles opposite the equal sides are congruent. If two sides, say AB and AC, are equal, then the angles at B and C are congruent—the base angles.

That’s exactly what the Isosceles Triangle Theorem states, and it explains why those two base angles are equal, no matter how the triangle is drawn as long as two sides are equal. The other ideas—base angles being supplementary, medians always perpendicular, or all sides being equal—do not describe this theorem: equilateral (all sides equal) is a different case, and the base angles being supplementary or medians always perpendicular aren’t general consequences of two sides being equal.