Question

Can two of the angle bisectors of a triangle intersect perpendicularly? Why?

I thought yes, because I think it works with an isosceles triangle.

Answer 1

Draw two angles, with their angle bisectors meeting at 90º angle

Answer 2

I claim angle a+angle b= 90

a is 1/2 the upper angle, so the upper angle is 2a
same for b, it's 1/2 the other angle in the triangle, which must be 2b
2a+2b= 180, and we have not added in the 3rd angle. So it looks like angle bisectors can never be perpendicular.