What I desire to execute in this video clip is prove to ourselves that vertical angle really are equal to each other, their actions are really equal to each other. Therefore let's have a line here and let's speak that i have an additional line over there, and also let's contact this suggest A, let's speak to this point B, allude C, let's speak to this D, and also let's call this appropriate over there E. And so I'm just going to pick an arbitrarily angle over here, let's say angle CB --what is this, this looks prefer an F-- edge CBE. What I desire to perform is if I can prove the angle CBE is constantly going to be same to the vertical angle --so, edge DBA-- then I'd prove that vertical angles are constantly going to be equal, due to the fact that this is just a generalilzable situation right end here. For this reason what I desire to prove here is angle CBE is equal to, I might say the measure of edge CBE --you will check out it in different ways-- in reality this time let me compose it without measure so that you obtain used come the different notations. Ns will just say prove angle CBE is same to edge DBA. Is same to edge DBA. So the an initial thing we know...the first thing we know so what carry out we know? We understand that angle CBE, and we recognize that angle DBC are supplementary lock are nearby angles and also their external sides, both angles, form a directly angle end here. Therefore we recognize that angle CBE and also angle --so this is CBE-- and also angle DBC room supplementary. I will just write "sup" for that. They room supplementary. Which means that angle CBE plus angle DBC is equal to 180 degrees. Same enough. We likewise know --so let me check out this is CBE, this is what we care about and we want to prove the this is same to that-- we likewise know that angle DBA --we understand that this is DBA ideal over here-- we also know that angle DBA and angle DBC room supplementary this angle and also this angle are supplementary, their outer sides type a straight angle, they are surrounding so they room supplementary i m sorry tells us that angle DBA, this angle appropriate over here, plus edge DBC, this angle over here, is going to be equal to 180 degrees. Now, from this peak one, this optimal statement end here, we have the right to subtract edge DBC native both sides and we gain angle CBE is equal to 180 levels minus angle DBC that's this info right over here, I just put the edge DBC on the right side or subtracted it from both sides of the equation and this best over here, if I carry out the exact same thing, subtract edge DBC from both sides of the equation, I get angle DBA is same to 180 levels --let me scroll over to the right a little bit-- is same to 180 degrees minus angle DBC. Therefore clearly, angle CBE is equal to 180 degrees minus edge DBC angle DBA is equal to 180 levels minus angle DBC therefore they space equal to each other! They space both equal to the exact same thing so us get, i m sorry is what we want to get, edge CBE is same to angle DBA. Edge CBE, i m sorry is this angle right over here, is same to edge DBA and also sometimes you can see that displayed like this; so angle CBE, that's the measure, and also you would certainly say the this measure appropriate over right here is the specific same amount. And also we have actually other upright angles whatever this measure is, and also sometimes friend will watch it with a twin line like that, that you deserve to say that THAT is going to it is in the exact same as every little thing this angle ideal over right here is. You will check out it written choose that sometimes, I prefer to use colors yet not all publications have the deluxe of colors, or occasionally you will also see it written prefer this to show that they space the exact same angle; this angle and also this edge --to display that these space different-- sometimes they will certainly say the they are the same in this way. This edge is same to this vertical angle, is same to its upright angle right over here and also that this edge is same to this angle that is the contrary the intersection appropriate over here.
You are watching: If two angles are vertical angles then they are congruent
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What we have proved is the basic case due to the fact that all i did below is I simply did two basic intersecting lines ns picked a arbitrarily angle, and also then I proved that the is equal to the angle the is upright to it.
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