Medal! Can someone please further explain what a perpendicular bisector is please? Is it something that divides a figure in half or something? Muchas gracias.

@EclipsedStar
@e.mccormick
@josedavid
@CausticSyndicalist
@sleepyjess
@Ashchu117

Question

Medal! Can someone please further explain what a perpendicular bisector is please? Is it something that divides a figure in half or something? Muchas gracias. 

@EclipsedStar 
@e.mccormick 
@josedavid 
@CausticSyndicalist 
@sleepyjess 
@Ashchu117

e.mccormick · Answer

Well, as you got, to bisect is to cut in half.  Now, what they call half could be by length or by area depending on the type... now, do you know what perpendicular means?

gottennis121 · Answer

Two lines that meet at a 90 degree angle (or right angle).

e.mccormick · Answer

Exactly!  Now, because these are going to be some line segments, where do you think you would bisect?  And it does not matter if what is being bisected is the side of a traingle, or other polygon.  It is still a segment.  So when you do a perpendicular bisector the bisect, or cut in half, has to be at a particular point.  Where is that point?

gottennis121 · Answer

At the 45 degree angle? Just to put if out there, the question in the test is "Explain how to construct a perpendicular bisector."

e.mccormick · Answer

An angular bisector would cut an angle in half, so it would divide the measure of the angle in half.  You can never have a perpendicular of an angle other than of 180 degrees.  A 180 degree angle is basically a line.  This is why you can only have a perpendicular bisector of some sort of line segment.  So where on a segment do you think it would happen for the word half to be involved?

e.mccormick · Answer

In other words, what is the special name for the "half way" point on a line segment?

gottennis121 · Answer

Sorry if I'm making this complicated, is it midpoint?

e.mccormick · Answer

Yes, the midpoint.

And no, you are not making it complicated.  I just want to be clear so that you remember it.  =)

e.mccormick · Answer

OK, so on ANY line segment there is a perpendicualr  perpendicular bisector.  It is at the midpoint and forms a right angle with the segment.


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e.mccormick · Answer

Now here is another intersting fact:

On any triangle, the 3 perpendicular bisectors meet at the midpoint of the triangle.
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e.mccormick · Answer

And, here is another bit of triabhle fun:  The angular bisectors also meet at the same point!
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