How to Construct a Quadrilateral when its four sides and one angle are given



welcome to education channel this video I am going to explain how to construct a quadrilateral when four sides and one angle is given okay let me write question first a construction of correlator so to construct any quadrant we need a minimum five measurements either four sides one angle or three sides two others so this see video is about four sides and one angle is given now question is like this construct a quadrilateral ABCD so in a be cyclic quadrilateral into constant here values of a b is equal to four point three centimeters angle a 60 degree and bc three point five centimeters CD two 0.89 ad is equal to three point three centimeters right so this is the question four sides and one angle is given first you will see it off diagram so we can take any one on this side which is given we should take as the base so to easy construction so if you take rock diagram so I need to construct a quadrilateral so these are four sides so I'm taking a b c d so an important thing when you are denoting the vertices either clockwise or anti-clockwise on doing it right okay there's a very important if your itlp should be see here okay not this AP and series wrong a CD clockwise or anticlockwise only need to write the vertices any other no in this rock diagram AP 4.3 and create 60 degree and bc 3.5 CD to 0.8 and 83.3 this is the given data we need to construct first of all we'll construct base four point three centimeters so a B so using the scale base we should take four point three centimeters first they will be four point three centimeters so no no no angry yayyy sixty degrees so by observing the rough diagram we can take on the one step now using compass we need to construct a sixty degree because four sides of an angle is given the time will come straight first sixty degree so try not with the same radius to cut this song because 60 degree now from a if you go to a to some point be easy with three point three distance now we can exchange this line and three point three cuts so you get the vertex thirty can join this so in this line only we have a 2d three point three centimeters now using compass take three point three centimeters distance using scale zero to three point three a duty because three centimeters three millimeters should take three point three distance from here to here from a it just to cut the arc on this plane because we know you to do only three point three centimeters so that is Cir D there's a D so here two DS three point three centimeters now next a B so somewhere here vertex is there but see if you want to find out B to see distance we know and D to see also we know the distance right so you have B to see three point five centimeters and D to see two point eight centimeters so – r2 should drop from be three point five centimeters radius because three to that C distance is three point or three point five so take B to three so three point five radius so it take now from be drawn on okay just try not now next to D to see you know D to C distance is too wide it again using scale take distance to or two point eight so zero to two point A to D that one we should take from D because D to C is two point eight centimeters so fun now take cut this up okay wait the two arcs will join that is the vertex C fine a B C D or we good now just to join using the scale or the vertices we can join B to C again this is a D point and need to see also just joining us simple now we can observe B – C is three point five centimeters and CD is two point eight centimeters and angle is 60 degrees so according to the given information exactly constructed no this is the way we can construct any quadrilateral when four sides and one angle is given so the triangle is given that side only we should draw us to because you can construct the angle directly so if you in case if we draw BC we cannot get B or C D directly there's not which angle is given the triangle concerned side only we need to construct so if angle a is given so either a B or a lyrical construct as the base so we can get the coordinating no steps of construction so if you want to know the steps of construction also I'm providing my link in description below there's a website so I can see our talk on the website name foundation for regular come in the website all the constructional classes and videos are will have the same thing can see the steps of construction by clicking their website and go through a cardio class face

Constructing the Circumcenter



one of the four main types of points of concurrency that we find in triangles is the circumcenter point of concurrency means you have at least three lines intersecting in one spot so the circumcenter is where the three perpendicular bisectors of each side intersect which also makes it the center of a circle that circumscribed about the triangle so if we take a look at a sketch of what a circumcenter might look like we notice that it could be a really big circle if you have an obtuse triangle and that it passes through all three vertices which means that the center is equidistant from the three vertices but when we ever apply this in real life well a common problem that you might see on a test is if they give you three different points and they say where's the treasure the treasure is located at an equal distance from three random points maybe a tree stump a gravestone and the beach so what you would do to find the treasure is you would have to find the circumcenter of the triangle by drawing those lines so what you would do if we erased this treasure is you would draw in your three sides of your triangle and then using your compass you would construct the three perpendicular bisectors of each side so there would be one perpendicular bisector and then here would be another perpendicular bisector and again this is just an estimate to show you how you would solve this problem and then here you'd find your perpendicular bisector and ideally by definition these points are concurrent as you can see I'm a little bit off but that's just because I was sketching so you would say that the treasure would have to be right here which is the center of a circle that passes through the three vertices

How to Construct a 45 45 90 Degree Triangle with a Compass



hi I'm Rachel and today we're going to be going over how to construct a 45-45-90 right triangle with the compass so a 45-45-90 is an isosceles right triangle well if we're making a right angle right a 90 degree angle we can use the compass we can put a point on the piece of paper and just use the ruler to draw a straight line or the part of the compass that's straight to do a straight line there then take the compass so that it forms a perfect 90 degree angle right and you do a point there and then you use your ruler to others or straight edge of some sort to do a straight line like such and that will give you a 90 degree angle then you bring the compass up into the dot and you see where is a 45-degree angle well 45 is half of 90 so it's going to look like just drawing you without a compass something like this right that's half of a perpendicular angle that would be right like this so this is 45 degrees I'll write it out here and this is also ends up being 45 degrees because that forms the perfect triangle and just so you know for the ratio of a 45-45-90 right triangle the sides will be X X and X root 2 in case you're going a little further and doing the sides after you've constructed it with your compass I'm Rachel and thank you for learning with me today

How to construct the circumcenter of a triangle in Geogebra



in this video we'll be constructing the circumcenter of the triangle again file save as name your file correctly make sure you know where you're saving it so you can upload it when you're finished go to view uncheck axis we don't need those today go to options labeling and let's go with no new objects once again start with a triangle any triangle somebody used the polygon tool and there is my triangle alright the circumcenter involves perpendicular bisectors perpendicular bisector and don't confuse it with the median don't confuse it with an altitude it's got a characteristic of each but it's different than most of them at the same time so it goes through the midpoint of this side and it's perpendicular to this side so I need the midpoint first so make sure you choose your midpoint tool get the midpoint of each side and see if you use your arrow tool those stay midpoints no matter how you manipulate it perpendicular bisectors now want the perpendicular line tool if it was an altitude it would be perpendicular to this bottom segment segment containing point a if perpendicular bisector may or may not hit point a it doesn't necessarily the point it hits is the midpoint so click a segment and click the midpoint of that segment click a segment and then click the midpoint of that segment and those are your three perpendicular bisectors you can see none of them are also altitudes because none of them hit none of them hit that vertex both altitudes and medians both come down from a vertex so these are not altitudes these are not medians these are perpendicular bisectors alright and you see your circumcenter right there let's go ahead and put that point in so I want the intersection of two objects pick two of your perpendicular bisectors it doesn't matter which one there's your circumcenter let's use the Move tool or the arrow tool to rename it right-click the point go to rename call it circumcenter okay alright well remember the circumcenter is equidistant from the vertices of the triangle hey and also as a circle that circumscribed about the triangle or I should say it's the center of a circle that's circumscribed about the triangle so I want to draw that circle and then we'll be finished circle tool there's a couple ways to make circles I can make a circle through three points we can actually use that in this case and use the three vertices of the triangle I could make it with a given radius I don't want to do that one because the radius is going to vary depending on what I do with my my three points I'll go ahead and use the center end point okay so you had after doing the right order first you choose the center of the circle and then you choose a point on the circle the center of the circle is the circumcenter point on the circle any one of the three vertices does not matter which one you pick okay you choose the arrow tool and drag this around you see that no matter what happens the center of the circle is always that point of concurrency the circumcenter and each one of the vertices is always on the triangle or as always on the circle hey if it's obtuse triangle the circumcenter is external if it's a right triangle the circumcenter is on the midpoint of the hypotenuse okay make sure you save your file and then upload it to school fusion

How to construct the incenter of a triangle in Geogebra.



in this video we'll be constructing the in center of a triangle using geogebra a few reminders file save as name your file last name first initial underscore in the center make sure you know what you're saving it in so you can upload it when we're finished go to view uncheck axes no need them go to options labeling you want no new objects I think I missed option is labeling no new objects ok draw my triangle okay now to draw the in center I need three angle bisectors the angle bisector tool is under this perpendicular line menu and I want and this listener is angular bisector same thing as an angle bisector to draw it I can click three points or just the two lines that form the angle so look quicker I think to click the two lines so I'm going to go with that you'll see when you draw it it drew two lines this one is the angle bisector and this one's it's perpendicular it's just kind of the way geogebra does it that's getting rid of that one okay right-click uncheck show object I don't want to lead it I just don't want to show it okay do the same thing for the other angles right click uncheck show object make sure you're not hiding the angle bisector you want to hide it's perpendicular okay all three should be concurrent at a point inside the triangle doesn't matter how I move this triangle it could be acute right or obtuse the in-center stays inside the triangle all right I'm gonna have some other lines in this picture so I want to change the color and style of these three hey if you want to select them in the outer window you see the objects that you hid on this white dot over here so if you want the ones that are still there click the ones with the blue dots that's confusing though I just hold down the control key and click them in the geometry window make sure they all highlight once all three of them are highlighted and you want to right-click color go with the red again style we're gonna make these dashed okay so there's your three angle bisectors let's put the in-center in go to the intersect tool click any two of those lines as a matter which two and you'll get your edge Center rename it by right-clicking and going to rename and we want to call it the in center okay for I finish I want to draw the inscribed triangle remember the in center is the center of a triangle or the center of a circle inscribed in the triangle hey the in center is equidistant from the sides of the triangle how do you measure the distance from a point to a line how far is this point from this line well I'm gonna have to draw perpendicular to measure that distance so choose the perpendicular line tool click this line and this point like again the in center and inside the triangle in center the side of the triangle and if you're lined your little chip goes together they're confusing you could move this around and try to space them out a little more but really shouldn't matter okay now I want points where my new lines intersect the triangle now this might be a little confusing you want to look for the ones that might be perpendicular okay so make sure going in the right direction in other words if I started the in center it goes to directions it doesn't look perpendicular here does it I want to go the one that the side that looks perpendicular you should be like visually tell so let's put those points in there I want to use the intersection tool again I want to intersect the side of the triangle okay make sure I've got the intersection tool selected let's take the side of the triangle and that line I'm gonna click the side of the triangle and that line and last the side of the triangle in that line okay all right now I can I can get rid of those lines I don't need them anymore I could ready to get rid of a bunch of objects over here on the right choose the show/hide object tool and it's gonna pop up with your head and objects and that's okay click these other lines that I want to get rid of click each one of them you don't have to right-click or anything like that just left click them and make sure they're all highlighted don't don't wreak lick any of the other ones that were hiding previously just click those three lines that I just drew and then change your tool to any other tool and everything disappears now my picture is a lot cleaner all right last I want to draw the circle a circle to the center and point Center is the in-center choose any one of these three sides or any three oh I'm sorry any any one of these three points and there's your inscribed triangle as I move the vertices around okay stays inscribed so it's touching each one of the sides at one point and that is an in center and it's corresponding inscribed circle make sure you save your construction and upload it into school fusion

Constructing triangles SSS



however young boys welcome to another video from me mr. Arnold in this video we're going to learn how to construct a triangle and given three sides or SSS side-side-side so I want to draw a triangle here of side length five centimeters six centimeters and seven centimeters I'm just going to start by drawing a side I'm going to draw the longest side here I'm gonna draw seven centimeters in length I'm gonna get my ruler and I'm gonna draw a line seven centimeters in length so let's get the pen tool and I want my life to be go from 0 up to 7 so now I'm just going to label that 7 centimeters now the next task is to get two more lines one five centimeters I'm one of six centimeters in order to do this I'm going to need a pair of compasses so I'm going to take up my compass tool as well so what we need to do is take my compasses and I'm going to line it up and measure so that it's 5 centimeters in total so we can see a compass is go from 0 to 5 so it's 5 centimeters in total let's just move the ruler out of the way now without changing the size whatsoever you want to move it down and line it up so that it touches the end of my line and then we're going to do is we're going to draw on arc so you're going to use your compasses and draw a nice big arc for me like so that's step one yeah we need to now draw an arc of six centimeters in length so I just turn my corpuses around and I would like this one to be six centimeters in length so I'm going to measure six centimeters using my ruler and compasses as you can see goes from zero to six and I'm going to line it up at the other end so let's start from here so the point is on the end of the line as you can see this is six centimeters in length and then we're going to draw a second arc so draw a second Eric around like so now we're almost done take my compasses away this point which I'll mark in red this point here is the key point that's the top of our triangle all I gotta do now control two straight lines one from here and from the other side and if you want when you're finished you can actually take away your construction lines or erase them using a river this side here should be five centimeters we'll measure in a second just to make sure this wood should be six let's just use the ruler to check so swim rig around and let's line it up that's zero yeah that looks good it goes from zero to five so that's five centimeters in length assume that the other side is going to be six again let's just make sure so from zero to six and that is how you can stroke the triangle when given three sides see you again sometime