Question

if in a triangle two bisectors are equal prove that the triangle is isosceles

Answer 1

Answer:

Assuming that the bisectors are inside the triangle....

Step-by-step explanation:

For isosceles triangle 2 angles

must be equal

Let's take  both bisected angle s

Let one angle be A and the other be B

Then,

A less than B (1)

A is greater than B (2)

A = B (3)

If A is less than B then bisector of A is larger than that of B because larger angle has smaller bisector but since both bisector are equal so this is not possible as bisector are given equal.

If A is greater than B then bisector of B is larger than that of A because larger angle has a bigger bisector but as both bisectors are of equal length then this isn't possible.

As both the first and second statements are wrong and that A=B then ,

the triangle has to be isoceles as only isoceles triangles have 2 equal sides(the angles on both bisectors are equal).

Hope this helps!!