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.

Video Examples: How to use Base Angles Theorem


Example on Base Angle Theorem

      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

Ques: 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. 108o, 36o, 36o
    B. 30o, 90o, 60o
    C. 40o, 62o, 78o
    D. 42o, 64o, 74o
    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, 108o, 36o, and 36o would be the measures of the three angles of the triangle.

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