Basic constructions for similar triangles

Añadido: 2026-05-05

[00:00:00]these are few basic constructions that you should know children here we have angle abc and the question is we have to draw angle pqr which is congruent to this angle abc so if i draw a rough figure i have angle abc here i have to draw angle p q r such that this angle is equal to this angle okay so let us see how to draw that first we will draw the ray qr so let us just draw the ray q r name this as q and r now let us see how to draw an angle which is congruent to angle abc first step open the compass any measurement which you want a small measurement preferably and then keeping the point as at b make an arc then without changing the measurement keep it at q and make an arc sorry again this is the arc now we have to take in the compass how much this angle has opened okay so keeping the compass at this point i will have to measure how much this arc has opened this angle has opened so i will measure it yes so this much correct this much this is the measurement of this angle so using this measurement we have to cut an arc on this one so keeping the compass at this point make a cut so you have got this same measurement now simply join q and this point so when you so when you join it you get p q r such that this angle is equals to this let us just measure it this angle is 50 degree let us see the measure of this angle this angle is also 50 degree okay so this is how you draw congruent angles next construction basic construction construct angle pqc congruent to angle abc now if you observe you have c point c common in both of them such that c q b are collinear c q will come somewhere here and b so if i draw a rough figure this is c b a q will be lying somewhere such that when i draw p q c this angle will be equal to this that is angle p q c angle p q c congruent to angle abc congruent to angle abc so this is the rough figure we have to draw it fair so let us say point q is somewhere here now we have to open up this angle same just like before how you drew congruent angles so from point b you have to make a cut using the same measurement from point q also you have to make a cut now using the compass see how much this angle has opened so keeping the point of the compass here measure how much so adjust the measure of the compass so that it intersects here okay so you can see the arc which i have made here it is exactly how much this angle has opened same measurement from this point also you make a cut so we have got this point here now simply just like before join q and this point so when you join q and that point you get the angle p q c which is congruent to angle abc let us check angle abc is 50 maybe 50 sorry yeah maybe 51 50 and 51. between 50 and 51 so even this one seems to be between 50 and okay so this is how you draw congruent angles if they both lie on the same line such that c q b are collinear c q b are collinear this is the next basic construction which you should know construct angle pqc congruent to angle abc again point c is common in both of them but we have this condition c b q are collinear c b q will lie somewhere here they are collinear so if i draw the rough figure it will be somewhat okay let me make it again this is given to be a b c point q a will be somewhere on the right side point q such that when i draw p q c the angle pqc will be equal to angle abc angle pqc this one congruent to angle abc which is this one so let us see how to draw that now as you can see q is lying away from point b so you will have to extend this so let us just extend this suppose my point q is here now we have to draw angle abc congruent to angle pqc okay so again same way how to draw congruent angles keeping the composite point b any measurement draw an arc using the same measurement keeping it at point q draw an arc okay now measure this angle how much this has opened so let me just check how much does open keeping the compass here adjust the compass so that you see fine so this is the measure this is the measure taking this measurement don't change this measurement taking this measurement now you have to make a cut here right and now simply join this point of intersection to point q let us join when we join we get p q c let us see if both are equal angle abc has come out to be 50 angle pqc has also come out to be 50 50. okay so this is how you draw congruent angles such that c b q are collinear that is both the angles are lying on the same line now let us see how to divide a given segment into given number of equal parts for example here we have segment a b equal to 9 centimeter which we have to divide into three equal parts let us draw the rough figure first suppose this is segment a b which is nine centimeter right now the first step which you do is you draw a ray from point a any measure will do just array now taking the compass you have to make three equal arcs on this ring this is your second step third step let this be point p1 p2 p3 third step join p3 to be point b now this angle which you have obtained here you have to draw congruent angles from point p to also and p1 also right so first step is what you have to make a cut from point p three one big arc using the same measurement from point p two also and from point p one also next you have to measure how much this angle is opening correct how much this angle is opening so once you open this angle this is the point okay this is the point how much this angle is opening so taking this measurement on the compass you have to cut here from point p to make a cut from point p one also to make a cut and then you join p two to this one and p one to this one so these three will be equal that is how you're going to do this now here i've already drawn a segment with length 9 centimeter let us see the remaining steps so first step let us name this as a and b and this is 9 centimeter let us draw array any measurement will do from point e right now using the compass take any measurement which you want any measurement will do but see to it that all three are equal so from point a you make the first cut using the same measurement from this point make a cut and using the same measurement from this point also make a cut so you've got three equal cuts let this be point p1 p2 and p3 next step is join p3 to point b now you have got an angle ap3b this angle you have to draw congruent angles at point p2 also and p1 also angles which are congruent to this angle so the procedure is same make a cut at p3 at p3 make a cut any measurement will do but once you take a measurement do not change it so without changing from point p to also and from point p one also okay next you have to see how much this angle is opening as always we will see how much this angle is opening so it's opening this much right so let us make first cut here so that you get an exact measurement so this is your first cut without changing now from this point you have to make a cut and from this point you have to make a cut okay now so you have got this as one of the point of intersection and this as one of the points of intersection so now simply join them p2 to this point of intersection so when you join you get this right so this is the point of intersection and here also when you join you get this now don't cross the line don't cross the segment even if the point is here don't join it till there because you need the point only on segment a b so this should be equal to this should be equal to this let us see it was nine centimeter so each part should be three centimeters so yes you have got a three centimeter then at six another three centimeter and at nine another three centimeter so these are the basic concepts which you should know in order to draw similar triangles okay thank you