base angle theorem


Definition of Base Angle Theorem

  • Base Angle Theorem states that if two sides in a triangle are congruent, then the angles opposite to these sides are also congruent.

More about Base Angle Theorem

  • Base angles of an isosceles triangle are equal.
  • Converse of the base angle theorem is also true, i.e. if two angles of a triangle are congruent, the sides opposite to these angles are congruent.

Example on Base Angle Theorem

  • In the given triangle, as the sides AB and AC are congruent, the angles opposite to these sides (∠B and ∠C) are also congruent.

Solved Example on Base Angle Theorem

The length of two congruent sides of a triangle is 6 cm. Which of the following could be the measure of the three angles of the triangle?
Choices:
A. 108°, 36°, 36°
B. 30°, 90°, 60°
C. 40°, 62°, 78°
D. 42°, 64°, 74°
Correct Answer: A
Solution:
Step 1: According to the base angle theorem, if two sides of a triangle are congruent, the angles opposite to these sides are also congruent.
Step 2: The length of the two sides of the triangle are congruent, so the angles opposite to these sides would be congruent.
Step 3: So, 108°, 36°, and 36° would be the measures of the three angles of the triangle.

Related Terms for Base Angle Theorem

  • Angle
  • Base
  • Congruent
  • Congruent angles
  • Congruent Triangles
  • Isosceles Triangle
  • Side
  • Triangle