11/18/2023 0 Comments Vertical angles geometry definitionWhich means that angle CBE plus angle DBC is equal to 180 degrees. So we know that angle CBE and angle -so this is CBE- and angle DBC are supplementary. So the first thing we know.the first thing we know so what do we know? We know that angle CBE, and we know that angle DBC are supplementary they are adjacent angles and their outer sides, both angles, form a straight angle over here. I will just say prove angle CBE is equal to angle DBA. So what I want to prove here is angle CBE is equal to, I could say the measure of angle CBE -you will see it in different ways- actually this time let me write it without measure so that you get used to the different notations. What I want to do is if I can prove that angle CBE is always going to be equal to its vertical angle -so, angle DBA- then I'd prove that vertical angles are always going to be equal, because this is just a generalilzable case right over here. And so I'm just going to pick an arbitrary angle over here, let's say angle CB -what is this, this looks like an F- angle CBE. So let's have a line here and let's say that I have another line over there, and let's call this point A, let's call this point B, point C, let's call this D, and let's call this right over there E. What I want to do in this video is prove to ourselves that vertical angles really are equal to each other, their measures are really equal to each other. This will always be true as no matter how much you rotate the line, in either direction, if you add to one angle you will always be subtracting that same amount from the other. notice that both angles still add up to 180 degrees. The angle on the right hand side of the line grows by ten degrees, and is now worth 100, and the angle on the left hand side shrinks by 10 degrees, and is now worth 80. Now imagine we rotate this line by say 10 degrees to the left. This now cuts our 180 degrees in half and we now have two angles both measuring 90 degrees on either side of the the perpendicular line. Now imagine we drop another line perpendicular to our original line. So we know that the measure of an angle between any two points on a straight line is equal to 180 degrees. We have now cut our original 360 degrees in half giving us 180 degrees. Now imagine we cut a line directly through the centre of the circle (a diameter). Along time ago the ancient Babylonians defined a circle to be made up of 360 degrees. By definition Supplementary angles add up to 180 degrees. This is proven by the fact that they are "Supplementary" angles.
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