Question

How to get the length of an angle bisector if it bisects an acute angle in a right triangle and cuts its opposite side in a ratio of length 1 and 2?

Answer 1

The Angle-Bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.The Angle-Bisector theorem involves a proportion — like with similar triangles. But note that you never get similar triangles when you bisect an angle of a triangle (unless you bisect the vertex angle of an isosceles triangle, in which case the angle bisector divides the triangle into two congruent triangles).