December 7th, 2016, 08:27 AM  #1 
Newbie Joined: Dec 2016 From: Dhaka, Bangladesh Posts: 9 Thanks: 0  perpendicular bisecting an angle
Let's assume a right triangle where ∠BAC =90° and a perpendicular has been drawn to hypotenuse "BC" from point "A". And this perpendicular intersects hypotenuse at point "D" such that ∠ADB and ∠ADC equal to 90°. Does this perpendicular bisects the angle ∠BAC? One video lecture says that this perpendicular does not bisect ∠BAC, i.e ∠BAD and ∠CAD are not equal, and they are not 45°. The link of this video lecture is given below: https://m.youtube.com/watch?v=zQXAtI...le&hl=en&gl=US Let's assume another figure where an equilateral triangle has been drawn inside a circle. Each angle Angle of that equilateral triangle is 60°. Central angle∠AOC drawn on the arc AC is twice the inscribed angle ∠ABC drawn on that same arch AC. Since ∠ABC equals to 60°, ∠AOC is 120°. A perpendicular has been drawn to line AC, bisecting the angle ∠AOC into two equal half, i.e ∠AOD and ∠COD are equal to 60°. And OD is perpendicular to AC. (These lines about equilateral triangle drawn inside a circle have been taken from a video lecture made by Khan Academy link of which has been given below). https://m.youtube.com/watch?v=UmiZK6...le&gl=US&hl=en In case of 1, perpendicular drawn from point A to hypotenuse "BC" doesn't bisect the angle BAC, and in case of 2, perpendicular drawn from point "O" to line AC bisects ∠AOC. Please, let me know when a perpendicular drawn through an angle to a line of a triangle bisects that angle and when it doesn't. 
December 7th, 2016, 08:56 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,415 Thanks: 1462 
The perpendicular bisects the angle if and only if the sides that form the angle have equal length.


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angle, bisecting, perpendicular 
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