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Current time:0:00Total duration:4:09

Geometric constructions: congruent angles


Video transcript

what we're going to do in this video is learn to construct congruent angles and we're going to do it with of course a pen or a pencil here I'm going to use a ruler as a straightedge and then I'm going to use a tool known as a compass which looks a little bit fancy but what it allows us to do and will apply using it in a little bit it allows us to draw perfect circles or arcs of a given radius you pivot on one point here and then you use your pen or your pencil to trace out the arc or the circle so let's just start with this angle right over here and I'm going to construct an angle that is congruent to it so let me make the vertex of my second angle right over there and then let me draw one of the Rays that originates at that vertex and I'm gonna put this angle in a different orientation just to show that they don't even have to have the same orientation so it's going to look something like that that's one of the rays but then we have to figure out where we put where do we put the other array so that the two angles are congruent and this is where our compass is going to be really useful so what I'm going to do is put the pivot point of a compass of the compass right at the vertex of the first angle and I'm going to draw out an arc like this and what's useful about the compass is you can make you can keep the radius constant and you can see it intersects our first two rays at points let's just call this B and C and I could call this point a right over here and so let me now that I have my compass with the exact right radius right now let me draw that right over here but this alone won't allow us to draw the angle just yet but let me draw it like this and that is pretty good and let's call this point right over here D I don't know I'll call this one E and I want to figure out where to put my Third Point F so I can define ray EF so that these two angles are congruent and what I can do is take my compass again and get a clear sense of the distance between C and B by adjusting my compass so one point is on C and my pencil is on B so I have get this right so I have this distance right over here I know this distance and I've adjusted my compass accordingly so I can get that same distance right over there and so you can now imagine where I'm going to draw that second ray that second ray if I put point F right over here my second ray I can just draw between starting at Point E right over here going through point F I could draw it a little bit neater so it would look like that my second ray ignore that first little line I drew I'm using a pen which I don't recommend for you to do it I'm doing it so that you can see it on this video now how do we know that this angle is now congruent to this angle right over here well one way to do it is to think about triangle BAC triangle BAC and triangle let's just call it D Fe so this triangle right over here when we drew that first arc we know that the distance between AC is equivalent to the distance between a B and we kept the compass radius the same so we know that's also the distance between EF and the distance between edy and then the second time when we adjusted our compass radius we now know that the distance between BC is the same as the distance between F and D or the length of BC is the same as the length of FD so it's very clear that we have congruent triangles all of the three sides have the same measure and therefore the corresponding angles must be congruent as well