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
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.
Quick Summary
- Base angles of an isosceles triangle are equal.
- Converse of the base angle theorem is also true: if two angles of a triangle are congruent, the sides opposite to these angles are congruent.
🍎 Teacher Insights
Use visual aids and hands-on activities to demonstrate the theorem. Emphasize the connection between congruent sides and congruent angles.🎓 Prerequisites
- Congruent Sides
- Angles of a Triangle
- Isosceles Triangle
Check Your Knowledge
Q1: In triangle ABC, AB = AC. If angle A is 50 degrees, what is the measure of angle B?
Q2: In triangle XYZ, angle X = angle Y. If XZ = 8 cm, what is the length of YZ?
Frequently Asked Questions
Q: What type of triangle does the Base Angle Theorem apply to?
A: It applies specifically to isosceles triangles.
Q: Is the converse of the Base Angle Theorem true?
A: Yes, if two angles of a triangle are congruent, then the sides opposite those angles are congruent.