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Question

If in the below triangle B = 60o, which type of triangle is it?

A
Isosceles Triangle
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B
Equilateral Triangle
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C
Scalene Triangle
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D
Right-angled Triangle
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Solution

The correct option is D Equilateral Triangle
According to question,
BO is perpendicular to AC and AO = OC

BO is cutting the base into half and is also perpendicular to it
BO is acting both as an altitude and median.

An altitude acts as a median only in an Equilateral or Isosceles triangle with AB and BC being equal in length.

For the triangle ABC,
Sum of all angles = 180o
Or, A + B + C = 180o
Or, A + C + 60o = 180
Or, 2A = 180o - 60o ( angles opposite to equal sides are equal)
Or, A = 120o2 = 60o

A = B = C = 60o
The above triangle is an Equilateral triangle

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