 Hello and how are you all today? The question says in each of the following give the justification of the construction also. Here the construction today we are dealing is, construct a triangle of size 4 cm, 5 cm and 6 cm and then a triangle similar to its size are two-third of the corresponding size of the first triangle. Now, here it is write down the steps of construction first and we will be constructing the triangle and then the similar triangle side by side. What we need to do first is let us construct whose size are 4 cm, 5 cm and 6 cm respectively. Let us first draw a triangle and the triangle as A, B, C measuring 6 cm, 5 cm and 4 cm. Now, what we do need to do next is, then the second step is to draw a ray AX making an acute angle with B, C on the side opposite to the vertex C. So, here let us make an acute angle with AB and name it as AX. Third step is to locate 3 points that is A1, A2 and A3 on AX so that A A1 is equal to A1, A2 is equal to A2, A3. So, we need to make 3 equal points over here. Let it be like this, let this be the first point, this be the second point and this be the third point. That is A1, A2, A3 such that A A1 is equal to A1, A2 is equal to A2, A3. The fourth point is to join and draw through draw a line sorry and a line through A2 parallel to A3B intersecting to join to which is intersecting AB at C. So, let us measure this angle and on making the same angle over here we have A2C which is parallel to A3B. Let us name this as B dash not C dash. Now, we will be drawing a line parallel to BC through B dash which will be intersecting AC at C down also. We have drawn a line through B dash parallel to line BC to intersect AC at C dash. Now, then B dash C dash is the required, now for justification we know that angle ABC is similar to triangle AB dash C dash as we have drawn a triangle which is similar to the original triangle. Therefore, we can say that dash is equal to A upon AC dash is equal to BC upon B dash C dash but C upon B dash C dash is equal to 2 upon 8 which is equal to 2 upon 3 upon AB dash equal to AC upon AC dash equal to BC upon B dash C dash equal to 2 upon 3. So, this is the reason for justification as it was required to answer in the solution who the construction is understood by you well have a nice day ahead.