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6-2 Bisectors of Triangles

Added May 24, 2018 •

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alright you guys so he just asked question for today Georgia Line 6 - 2 which is really just going to be more review of what we spent doing on Tuesday and Wednesday bisectors of triangles and your son's question is what conjectures can you make about the perpendicular bisectors and angle bisectors of a triangle nose these keywords perpendicular bisectors and angle bisectors they keep coming up like every day because they're pretty important and you should know them for this chapter okay so I know the difference between two of them so when you guys are ready posit here I'm going to go ahead and keep going and here's your warm up for today so positive here cuz next thing is Ernestine a minute will be your answers you and your partner should be able to do these no problem these are like the last day of your notes from yesterday okay guys so here are the answers to your warm-up for number one if DC is 6.9 then that means the other side da is going to be 6 points number to equal to each other because they're equal x equals 4 but just don't forget to plug it in because they did ask you to find CD for number 3 because these two pieces are congruent then that means your angles are congruent so if one of them is 39 they're both 39 for the measure of ABC at 39 + 39 together and you get some alright so for the next part artegon this is what we've already been talking about this shouldn't be any new information for you except for this word concurrent and point currency of concurrent means that there are three or more lines or Rays or segments that intersect in the same point so when three or more parts come together and me at one point that's called concurrent and the point that they all meet at that's the point of concurrency I know math is really really great at. and we've already talked about one point of concurrency and that is where your perpendicular bisectors me and your perpendicular bisectors meet at the circumcenter and remember the circumcenter is equidistant from the vertices which means in this picture here BP is congruent to AP is congruent to peace be also remember that if this is the if this is the circumcenter they're also 90° and congruent on all sides cancel all the lines are equal to each other and then the perpendicular bisectors the blue lines it cuts your size in half and mates 90° alright so let's look at some problems so far it's extra example number one I just wanted to find what PA is in what the value of PA is and so here I noticed first of all the fees are all perpendicular bisector perpendicular same on both sides perpendicular same on both sides which means that this line is congruent to this line because she brought to this is congruent to the fly that means that PA equal 13 because the circumcenter is equidistant to the vertices get on your homework you don't have to write that sentence out I'm trying out for your nose also so that you hear me say it and you read it down a whole bunch of time and hopefully you remember okay the circumcenter is made up of your perpendicular bisectors and they are equidistant to the vertices another example little bit harder one more things to find so this one says find the length of p a second over here h c and b e alright starting off with p a well first of all I see over here that PB is 15 and see how it goes from the circumcenter to the vertex slap means circumcenter the vertex that means that PA is also going to have to be 15 cuz it is equidistant to the roots all right HC we have to do a smidgen. math HC is this piece right here and I noticed that I have 17 and I know this size is equal to 6 size Savannah the whole thing 17 and I want to find just one side what am I going to do divided by 2 so much is 17 / 2 and that gives me 8 and last but not least be and I'll be actually takes a little bit more amount of math and this is something I want to find out cuz you needed it for your homework last night B is the segment right here and well what do I notice about that right there what type of triangle is that triangle on what famous guy came up with him about right triangle Pythagoras I realize right now I don't have to talk to you later it's okay I'm so Define to be enemies x squared + 14 squared equals 15 squared K cuz 15 has to do is the longest side and so that one has to be seat so x squared plus I'm guessing this is one musics you guys could double check that for me make sure that you guys get the right work down on me notes x squared equals 25 for I think that's 29 again you guys should be checking this math cuz I'm not totally sure it's right I don't have a calculator on me and then final answers square root x equals square root 29 because 29 is just 29 and 1 it does not simplify so the length of bet is bad 29 so still right triangles are coming back and Pythagorean theorem just really dust doesn't go away in Geometry so anytime you find a right triangle try and see if you can do the factory in theorem okay if you guys need to continue to copy this down go ahead and posi you're otherwise I'm going to go ahead and keep going okay so I think I mentioned to you guys at the orthocenter could be outside of the triangle but I also wanted to show you guys that the circumcenter could also outside the triangle also circumscribed is when a triangle is inside a circle and the circle is around outside of the triangle I said if that would be inscribed and inscribed would be when the circle is inside the triangle and so I was just showing you some different versions of what this might look like so I like this right here it's outside the triangle but is the circumcenter and circumcenter because circumscribed see how they can start with the same word anyways next part in Center so the in-center is the point of concurrency of your angle bisectors or it's where all your angle bisectors meet that's your in center and you're in Center is equidistant from the sides of the truck so then this is all stuff that we already took notes on stuff that you guys should kind of be somewhat familiar to see me by now because we've done it so many times and so many days in a row but just in case you're not wearing right down again and I'm going to keep saying it over and over again so again the in-center is equidistant to the side and we should make note that they have to be the 90-degree angles for your s Center answer your perpendicular bisectors are equal to the vertices and your in-center is equidistant to the sides so we have these examples here in the figure shown and D equals 5x minus one I was going to come on Arrow cuz I don't got no space to do that 5 x -1 and any is 2x + 11 alright well since these are all angles bisectors cuz you can tell because they got the little arcs in them so that means this is the in-center text sorry that that was terrible in Center because angle bisectors any better anywhere in that part of the angle bisectors which means that for part a 5x - 1 equals 2x + 11 -2X from both sides add once both sides and 3x equals divided by 3x equals 4 but it said find and asked was it turns out and  is also the same as Amy is also the same as and deep so I'm just going to plug it in it doesn't matter which one you plug it in for cousin are the same so NF equals I'm just going to go get into five cuz I like five nights at 5 * 4 - 120 - 1 is 19 so NF equals 19 I'm in Part B it was just kind of like a bonus question and it says can mg so this line right here B18 explain your reasoning so talk it over with your partner jebaited out can that line B18 why or why not and the fact that this is 19 is important to know posit discuss it so hopefully you guys said no Angie cannot equal 18 because FN is shorter Angie and already an FN already equals 19 hey so can't be 18 since the shortest one is already 19 which is more than 18 so it doesn't make sense for it to be smaller when there's already one that's the smallest all right it's like a glass problem when your notes I think so in the figure q m is 3 x + 8 actually you and your partner and go ahead and you guys do this one first the next two years are going to see her your answers are you guys here my work and final answer so suddenly equal to each other I got x equals 1.5 or 3 over 2 and final answer for qpi. 12.5 just to show you guys at I can't get decimal answers even on your nose and on your test quit stop doing to your test just because you got a decimal answer you're probably still write most of you guys know what you're doing alright go ahead and get started on your homework find

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6-2 Bisectors of Triangles

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