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Isosceles triangle example
Question:
In triangle ABC, AC > AB. D is a point on BC and AB = AD = DC. If the angle C is 26o, what is the degree measure of the angle B?
isosceles triangles example.
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 = 26o
so angle DAC = angle C = 26o
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(26o) = 52o
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 = 52o
so the degree measure of the angle B is 52o
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.