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

welcome to educational channel this video I am going to explain how to construct a rhombus when one side and one angle are given how to construct the rhombus we'll see so since our question construct ABCD rhombus ap for centimeters so one side is given and one angle is 45 degree so when you see the properties of promise in rhombus all the sides are equal and opposite angles are equal every set is equivalent only opposite angles are equal so if I angle a is 45 degree for a opposite to angle C or so for D vertical so observe the raft diagram a B C B so a B for centimeters and angle is 45 degree so I was you take the which is given side you can take as a base and they however it is a b c d Sangre is 45 degree so anyway just take a reflector now a B is given four centimeters so four centimeters line segment will draw first and angle is 45 degree so it just observe the rough diagram and according to given data first we will draw a line segment a B that is sub four centimeters a B is 4 centimeters now angle a 45 degree first we'll start with 45 degrees and he a don't to construct for to be degree we need to construct was 90 and bisect it so if you are 90 we need to draw to our 16-month on the first draw an arc from this point 60 again from this point cut this 120 degree 60 and 120 if you bisect 90 degree will come first I think this if you join you'll get 90 degree line first so here this is the 90 and it is zero 9100 295 Isaac you'll get four to a degree from here draw an arc and from this end 0 60 90 120 90 n0 you should pass it then we get exactly 45 degree line so this is the 45 degrees from at the point here so angle a is 45 degree now if you observe a 2d is 4 centimeters because sin rhombus all the sides are equal maybe we need to get C and D so take the compass from 8 to 4 centimeters are killed wrong so A to B and this point is exactly equal to this 80 now this is B now somewhere seized it but B to C and D to C also same distance because all the sides are equal now whatever it is C a B or e a D same from D try knock and same 4 centimeters on me from the BR so draw an arc so maybe join that is so C and then join me scale all the surfaces join that you can join the NCOs so ABCD is a rhombus no then AV is the four centimeters and I am is forty by DT so account the properties firmly we need to apply because every side is equal in this so we do see also four centimeters this also for and it is also four centimeters and opposite angles are equal if angle a is 45 and the C also fortified so this way we can construct rhombus and one side is a nun angle is given and steps up this constitution of this video and providing on link in description below I will see the website name so in that website you will see a contact class ways not only constructions are there materials of other subjects also available already can go through the steps of transverse and directly next

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

in this video we're going to look at constructing a 30-degree angle to construct a predatory angle you're going to need some equipment first we're getting the pair of compasses and a pencil also I'm going to be using a straightedge or ruler to join up the lines as well okay so there's two different ways you can construct your pretty degree angle one way is to construct an equilateral triangle and then to do an angle bisector alternatively construct a special type of rhombus and then they would have a 30 degree in that and we're going to do both types in today's lesson so first of all let's do the equilateral triangle effort so what I'm going to do is I'm just going to draw a line of any size at the bottom okay so how much you can draw a 600 or line like so okay now get your compass put the point of your compass on the end of the line like so and for the pencil on the other end okay let me to every point on this arc is the same distance from this point here now if I do it from the other side make sure pencils on the end of the line and again draw it like so so if I join this point to here and this point to here you would have an equilateral triangle okay now we don't want to draw the whole equilateral triangle what we're going to do is we're just going to join from this point to the top so in doing so that's part of an equilateral triangle if I were drawn from here to here that with the complete equilateral triangle so therefore this must be a 60-degree angle okay now what I'm going to do is I'm going to do an angle bisector in this angle okay so what's the video an angle bisectors nine so again the point on the corner till arc they're an arc there I lift it up then arc towards the middle somewhere and arc towards the middle somewhere and let's join those up so there we have got a 30 degree angle so that's one method let's look at the rhombus method as well my just measuring it with a protractor as you can see we've got our 60 degree angle may have got our two 30 degree angles there and there so there we go okay G do the rhombus method to get the 30 degree angle I've just started off by drawing our line that's the six centimeter line and though it could be just once drawn on the page for you already I'm I'm just going to put my pencil and compasses the legs act limb for the line so you go and sleep a bit longer okay I'm going to do an arc like so and go into the over side I'm going to do arc like sir okay so similar to my equilateral triangle I have I suppose that would be an equilateral triangle now what I'm going to do is keeping the compass exactly the same size I'm going to do the arc over this way I'm putting the point of the compass down here I'm going to do an arc over this way so as you can see okay if I if you were to join up here to here to here to here that would be one equilateral triangle and from here to here to here that would be another equilateral triangle so therefore we've got a rhombus because all the sides would be the same length on the outside okay and so if you join this point in this point it would cut the 60-degree angle exactly in half down here so all your going to do is join from here to here and I won't necessarily want to draw the whole line you could just draw a part of the line but your part of the line if you want to you could draw the whole line across but then this angle here would be a 30-degree angle okay the future one all the way or your part of it and that would be a 30-degree angle let's just get the tractor metric just make sure so as you can clearly see it's a 30-degree angle so to recap this one put the compass point draw a line set the compass in the pencil so it's the exact way for the line to an arc and an overarching me both sides now we give you the equilateral triangle if you were to join it now put your compass here did an arc over this way and put your compass here put an arc in the same direction and then join up or draw a line that would join up the two opposite corners and then that would be a pretty degree angle and I'll see I'm just going to label it Fredi degrees just sure

this video we're going to be constructing angle-side-angle triangles or drawing them so we're going to be drawing or constructing angle air s air triangles and here you've got an a a triangle and angle the side in between the angles and the angle so a s a triangle so let's draw this what I would do is start by drawing the it centimeter line on the bottom then measure the 50 degree angle this way measure the 70 degree angle that way and draw two lines and where the two lines intersect will be where the top of the triangle will be and then that's the triangle draw okay so step one draw the eight centimeter line make sure this is really perfect really accurate yep exactly at centimeter okay then we've got a 50 degree angle on this side so we put our protractor and our zero on the line make sure it's absolutely perfect and measure around the 50 degrees so zero is here on the inside so we're going to go around 250 here so it's going to be exactly there okay so get your runner on draw a nice straight line through that point okay now the other side is a 70 degree angle so get your protractor again and put it on the other side the line of the Sun go to by 70 degrees is I'm put a mark so is there around 270 okay again get your line up with the end of the line and the point for a nice line for it now obviously you've drawn a bit extra depending on the question and if it tells you to leave the lines leave them you may rub the matter if you wish but now let's just label it so that's going to be 8 centimeters on the bottom this angle on this side is going to be 50 degrees like we measured and this one was 70 degrees and you can rub that out if you wish I just have a rubber here and then that's it that's your angle side angle triangle

the key points to an angle bisector is that it does almost lost dirt is that it does a couple things the first thing is it bisects the angle creating two congruent angles so if I have an angle that's in blue here and the red ray is my angle bisector then it has created two congruent angles so notice that this red is a rape so that's another key thing now it also could be a line segment if you're talking about something in a nice ah sleaze triangle perhaps perhaps so we could say or a line segment and every point along this bisector is the same distance from the two rays that make up the sides but how do we measure distance well the shortest distance from a point on this ray to a ray that forms the angle is along a perpendicular so if you're to construct the perpendicular from the angle bisector to a side and if you did that down here then you would say that these two segments are congruent so that's the key parts to an angle bisector is that bisects the angle creating two congruent angles that it is a liner or it is a ray or a line segment and that every point on this ray is the same distance measured along the perpendicular from the Rays that make up your angle but how do we actually construct them well to do that let's grab our compass and our straightedge and head over to this angle right here so we know that we're going to create a ray that creates two congruent angles so the first thing you're gonna do is you're gonna swing an arc just like if you were duplicating an angle so from the vertex I'm going to swing an arc so that I create two points of intersection now I want to create a point out here that is the same distance from these two points of intersection so if you want to you can change your company but you don't have to for the sake of argument I will and you're going to swing an arc from each of these end points so there's one arc from this intersection here's another point of intersection that I'm going to swing an arc from now this point right here is the same distance from both of these endpoints so I'm going to connect this point of intersection with my vertex thereby creating my angle bisector so I'm going to draw this connect my vertex and that point of intersection and what we've created are two congruent angles then when they sum you get the angle that you started with

welcome to education channel this video I am going to explain you how to consider to nineteen ninety degrees using only compass how to construct 90 degrees angle with compass and explain first we'll take a line segment now at this point at this point I want exactly consider to a 90 degrees angle so what you take first this from this point any point this is an American construct 90 degrees so I'm going to concerts night right to say I mean 90 degrees line there's some reasonable radius so don't take more than a very small take some radius and this is a center point and drawn out actually 90 is off of the 180 right 180 divided by two is ninety if I can find out 180 degree point then I can buy 6 0 and 180 from here I draw a not without changing the radius previous how much until you drop how much radius you are drawn without changing this now me here cut this arc and again from this point became Amarok again from here one more on that means this is 60 degrees and this is 120 degrees and remaining is 180 degree now this is a zero point and this is 180 degree point right now 0 and 185 bisect then 90 will come need not to extend the line at this point I want know this is the a so at the point yeah I mean 90 degrees so from a troy log first 60 120 and 180 three arcs if I got now from 0 and this one zero and 180 I have to bisect so from zero just take more radius draw an arc a bow because I am visible again same radius from 180 mark because I'm bisecting zero and 180 so 90 we come the simple logic 0 arc and from our nadh on dry not with the same radius no wait they join the both points just to draw a line from the now this angle if you keep the point C so angle B is exactly 90 degrees so you can check with protractor I kept it so exactly 90 degrees so this is the way we can construct until 90 degrees at any point okay we'll check from this is right curves one more thing I'll show you one more example I would construct 90 degrees they said awesome so what we'll take from the center point we just draw an arc right with the same radius factor to us and from yeah so zero point and one negative point in extent zero and 180 so I need to bisect this now this is 180 point cut our kaboom and from here be same they both both six from the zero point and 180 point and then joy if we join the two points so this is the angle 90 so you can use any side any way to not only these any line segment is given at any point we can construct 90 degrees using compass

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