The bisector of one angle of a triangle always separates the triangle into two smaller and congruent triangles.

Question

Quizplus · Accepted Answer

The bisector of an angle in a triangle divides the opposite side into segments that are proportional to the adjacent sides, but it does not necessarily separate the triangle into two congruent triangles. Congruency would require all corresponding sides and angles to be equal, which is not guaranteed by merely bisecting an angle.

The Bisector of One Angle of a Triangle Always Separates