## Construct Congruent Angle 2.m4v

let's construct a congruent angle I have angle XYZ it's a fairly large angle the first thing I need to do is give myself a nice straight rate to work from so I'm going to use my straightedge I'm just gonna get myself a nice ray okay so we made ourselves a nice rate of work from this could also be like our endpoint Y here I'm going to take my compass and I need to start from Y open the compass a comfortable amount and draw a nice arc through both rays now I'm going to keep the same compass setting it's really important that I not change that I'm going to come down here put my compass point on my new Y and I need to make a mark that's visibly larger than the other one see how much bigger that is now what I'm going to do is use my compass as a measuring tool and I'm going to measure this arc inside the two rays so I need to really be careful about adjusting my compass and see how I make that nice Construction mark there well I'm going to come down from this point of intersection I'm going to make a similar construction work and now this piece of art and this piece of arc should be the same length what that means is when I use my straightedge and my writing utensil going through this point through the point of intersection I have now created an angle here who is congruent to this angle here and since this is angle XYZ I could also call this angle XYZ because they are the same size they are congruent

## How to Constructing a parallel line through a point with compass and straight edge

okay through a point outside a line there's exactly one line parallel to the given line so I'm going to control this construction with the help of some software here so I've got a line and I've got a little smiley face that represents the point not on the line so the first thing we need to do we're gonna actually construct corresponding angles for this construction so the first thing we need is a line a transversal that passes through that point in that line so I'm just gonna draw in a transversal could be anything and we'll just have it kind of go through the middle of the point there so I've got a transversal that's the first thing you need to do you draw your line you draw a point not on it you draw a transversal through that okay the next thing we need to do is take your compass whoops and I need to be this one so take your compass and not that point and stick your point and I'm gonna spread my compass out just a little bit here and I'm gonna stick my point there and I'm gonna make an arc whoops without moving my line I'm gonna make an arc through the line we want parallel and through the transversal then I'm gonna move my compass up here to my points and make that same arc so you kind of see the corresponding angles forming okay then I'm gonna go down here and measure that arc on the bottom so I'm gonna spread this out a little bit and rotate it okay so I've got it kind of close I'll slide this in right there maybe a little closer okay so once you have that measurement then you go up here to the to the point where that arc intersects up above and you and try not to move that there we go and make an arc that represents the distance of the other arc so there we have it and now it's just a matter of drawing in that line and I'm gonna show up so I'll just have to go get a line and I'll connect that point to that that X to that point and there is my parallel line construction

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## Angle Bisector How to Construct Using Compass (Geometry)

here and what we're gonna do is we're gonna find the ray that bisects or cuts this angle in half so what we're gonna do is we're gonna open up our compass okay we're going to put this point here at the vertex so let me just rotate the paper a little bit here for us okay and what we're going to do is we're going to draw an arc here and here so it intersects the two sides of the truck of the angle if you want you can just draw one continuous arc so I'll just do that like so and then what we're going to do is we're going it use this point and this point those two points of intersection to make two more arcs so I'm going to go back here okay I'm gonna make an arc and what I usually do is I make the arcs just a little bit longer than I think that I'm gonna need because I want to make sure that they they intersect so I used that intersection point now we're going to use this intersection point over here notice I didn't change how open or close the compass was I kept that the same and I'm going to draw another arc okay like so and now what we're gonna do is we're gonna draw a ray through this vertex point and this intersection point and that's gonna be our angle bisector so let's go ahead and do that okay there you go so you can see that this angle right here is the same as that angle right there and you can use a you know a protractor to verify that but you can see it's going right down the middle its bisecting the angle cutting it in half I'll see you in the next video