Question
Find the type of the ∆ ABC if angles B and C are equal
- Right-angled triangle
- Equilateral triangle
- Obtuse angled triangle
- Scalene triangle
Hint:
In geometry, an equilateral triangle is a triangle in which all three sides have the same length.
The correct answer is: Equilateral triangle
In ∆ ABC, ∠BAC + ∠ABC + ∠ACB = 180° (Angle Sum property of triangle)
⇒∠A + 2∠B = 180° ————- (i) (Since ∠B = ∠C)
Also, In ∆ BOC, ∠BOC + ∠OBC + ∠OCB = 180° (Angle Sum property of triangle)
⇒∠BOC + 
∠B + ∠C = 180° (BO and OC are angle bisectors)
⇒ 120° + (∠B + ∠B) = 180° (Since ∠B = ∠C)
⇒ (2∠B) = 60°
⇒∠B = 60°
⇒∠C = 60°
From equation (i), ∠A + 2 x 60° = 180°
⇒∠A = 60°
∠A = ∠B = ∠C = 60° ⇒ ∆ ABC is an equilateral triangle
Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.
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