BOC is an isosceles triangle.
What is the isosceles triangle?
An isosceles triangle is a triangle whose two sides are equal in length.
Here given that ABC is an isosceles triangle in which its two sides AB and AC are equal.
⇒ AB = AC
In a triangle, if two sides are equal then the opposite angles of the triangle are equal in measurement.
⇒m∠ABC = m∠ACB
As.BO and CO are the angle bisectors of angle ∠ABC and angle ∠ACB respectively.
As BO is the angle bisector of the angle ∠ABC
⇒ ∠ABO= ∠OBC= (1/2)∠ABC
As CO is the angle bisector of the angle ∠ACB
⇒ ∠ACO= ∠OCA= (1/2)∠ACB
From the above it is clear that
m∠ABC = m∠ACB
dividing 1/2 on both sides
⇒(1/2)m∠ABC = (1/2)m∠ACB
⇒∠OBC= ∠OCA
In a triangle, if two angles are the same then their opposite sides are also the same in length.
⇒ OC=OB
⇒ As two sides of the triangle are equal then triangle ΔBOC is an isosceles triangle.
Therefore triangle ΔBOC is an isosceles triangle.
Learn more about the isosceles triangle
here: https://brainly.com/question/1475130
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