 Hello Owen, how are you all doing today? The question says draw a triangle ABC with size BC is equal to 6 centimeter, AB is equal to 5 centimeter and angle ABC equal to 60 degrees. Then construct a triangle whose sides are 3 by 4 of the corresponding sides of the triangle ABC. The steps of construction are as follows. The first step is to draw a triangle ABC where BC is equal to 6 centimeter, AB is equal to 5 centimeter and angle ABC equal to 60 degrees. Now this construction you have already learned in your previous classes so we have already drawn this required triangle for you where BC is 6 centimeter, AB is 5 centimeter and angle ABC is equal to 60 degrees. Now the second step is to draw any ray BX making an acute angle with BC on the side that is opposite to the vertex A. So we have a ray BX making an acute angle with BC which is opposite to the vertex A. Now in the question we are given that we need to construct a triangle whose sides are 3 fourth of the corresponding sides right? So we will locate 4 that is the greater of 3 and 4 is 4 in 3 by 4 right? Points that is B1, B2, B3 and B4 on BX such that BB1 is equal to B1B2 is equal to B2B3 is equal to B3B4 right? So we have this BX we need to locate 4 equal points let this be B1, B2, B3 and B4. Now we will be joining B4C and we will draw a line through B3 that is the third point since 3 is being smaller of 3 by 4 in 3 and 4 in 3 by 4 parallel to B4C intersecting BC at C dash right? So we will be joining B4C firstly and now through B3 we will be drawing a line which is parallel to B4C intersecting BC C dash this point will be C dash. Now we will draw a line parallel through C dash parallel to the line CA to intersect BA at A dash. So now we will be drawing a line which is parallel to AC intersecting AB at A dash. So A dash BC dash is the required triangle so this is our required triangle. Now for justification we have drawn triangle A dash BC dash similar to triangle ABC right? So this implies that A dash B upon AB is equal to sorry A dash B dash upon AB is equal to A dash A dash B upon AB is equal to A dash C dash upon AC is equal to A dash C dash sorry is equal to BC dash upon BC but we know that BC C dash upon BC is equal to is equal to BB3 upon BB4 which is equal to 3 by 4 so that means this whole will be equal to 3 by 4 and this is the required justification for the construction that we have done earlier. So hope you understood the whole construction well. Do take care while doing it and have a very nice day ahead.