Question

How to prove that the lengths of perpendiculars from any point on the bisector of an angle to the sides are equal.


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Answer 1

Answer:

the bisector of an angle is constructed by drawing a line through the set of all points that are equidistant to the two sides of the angle. So the distances are equal by definition. ... Then, with X and Y the feet of the perpendiculars from D to sides AB and AC respectively, triangle AXD and AYD are congruent (ASA).