Can two angle bisectors in a triangle be perpindicular. why?

Answer 1

try this: Let A1 , A2 and A3 equal the 3 angles in the starting triangle. So A1+A2+A3 = 180. Now you want to bisect two of these angles and have the remaining angle be 90. A1/2 + A2/2 + 90 = 180.
Solve these two equations by substitution and I get A3=0 which defines a triangle that does not exist. This I believe is true for angle bisection not segment bisection.

Answer 2

No, they cannot.

Think about it this way. Draw two lines that are perpendicular. Now try to draw a triangle around them using their endpoints as angle vertices for two of the triangle's angles.

You can't do it, because you always end up with a right triangle that has as two of its sides the very lines you drew to be angle bisectors.

Even if you start with any of the 3 types of triangles, you can't draw the bisectors without creating new triangles. And the only lines that are perpendicular are the sides of some of the triangles.

Answer 3

If we select the base of the triangle as a perfectly horizontal line it makes it much easier to see. The angle bisectors coming up from the bottom left and right corners must come up at 45 degrees from the horizontal base to be perpendicular to each other. For them to be at 45 degrees, the angles would have to be 90 degrees making them parallel to each other. The triangle could never be formed when two sides are parallel to eah other.