Question

prove that prependiculars drawn to the arms of an angle from any point on the bisector of angle are equal

Answer 1

Since the line of the angle bisector divides the angles equally made by the two lines, therefore, any given point on the angle bisector will be equidistant from the sides of the angles thus the line of the angle bisector is equidistant to the sides of the angle madeDraw the angle and the angle bisector. Take any point on the bisector and drop perpendiculars from that point onto the two arms of the angle. Now you have two triangles formed by the two arms, the bisector and the 2 perpendiculars that you drew. The two triangles are congruent because two angles are equal (the bisected angle) and the right angles and one side is common. Hence the perpendiculars are equal in length and thus the angle bisector is equidistant from the sides of the angle.

Take any point on the angle bisector and then drop two perpendiculars on the two arms of the angle

Then 90° =90°

its angle bisector both angles will be equal

One side is common

Answer 2

Answer:

Step-by-step explanation: