- Isosceles triangle example
- Question:
- In triangle ABC, AC > AB. D is a point on BC and AB = AD = DC. If the angle C is 26
^{o}, what is the degree measure of the angle B?

- Solution:
- since AD = DC (Given), so triangle ADC is an isosceles triangle
- In an isosceles triangle, two base angles are equal
- angle DAC = angle C
- Given: angle C = 26
^{o} - so angle DAC = angle C = 26
^{o} - since BDC is a straight line, so the angle ADB is an exterior angle of triangle ADC
- so angle ADB = angle DAC + angle C = 2 angle C = 2(26
^{o}) = 52^{o} - this is because an exterior angle of a triangle is equal to the sum of two noadjacent interior angles
- since AB = AD (Given)
- so the triangle ABD is an isosceles triangle, its two base angles are equal
- so angle B = angle ADB = 52
^{o} - so the degree measure of the angle B is 52
^{o}

- remark:
- In a triangle, if two sides are equal, then the triangle is an isosceles triangle
- In an isosceles triangle, two base angles are equal.
- In a triangle, congruent sides opposite congruent angles.

If two sides of a triangle are equal, then the triangle is an isosceles triangle. In a isosceles triangle, two base angles are equal. In other word, congruent sides of a triangle opposite congruent angles. An exterior angle of a triangle is equal to the sum of two noadjacent interior angles. From two congruent sides of a triangle, find which angles are opposite these two equal sides, then the two angles opposite the equal sides are equal.