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: 16,605 Thanks: 1201 
The perpendicular bisects the angle if and only if the sides that form the angle have equal length.


Tags 
angle, bisecting, perpendicular 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The smallest angle in a triangle is 1 5 15 as large as the largest angle. The third  GIjoefan1976  Algebra  4  February 16th, 2016 01:55 PM 
Simple(?) proof on points on bisecting lines.  Submerged06  Geometry  2  November 17th, 2015 07:49 PM 
prove that angle formed at orthocenter is supplement of the angle formed at the vertx  randomgamernerd  Geometry  2  November 17th, 2015 09:03 AM 
Calculating angle sin and sin angle without any functions.  Gyiove  Algebra  1  February 26th, 2014 05:57 PM 
Perpendicular  Gatu  Algebra  5  August 28th, 2007 09:19 AM 