 Hello and welcome to the session. In this session we discuss the following question which says construct a triangle ABC in which BC is equal to 6.5 centimeters, AB is equal to 4.5 centimeters and angle ABC is equal to 60 degrees. Construct a triangle similar to this triangle whose sides are 3 fourth of the corresponding sides of the triangle ABC. Let's proceed with the solution now. We'll do the construction step by step. First of all we'll construct the triangle ABC. So our first step of construction would be draw a line segment AB equal to 3.5 centimeters. This is the line segment AB of length 4.5 centimeters. Now in the question we are given that angle ABC is equal to 60 degrees. So in the next step we make angle ABY equal to 60 degrees at the point B. So this is angle ABY equal to 60 degrees. Now next we have BC is of measure 6.5 centimeters. Then in the next step with B as the center and radius 6.5 centimeters draw an arc on the ray BY. So we have drawn this arc taking B as the center and radius equal to 6.5 centimeters. Let this point of intersection of the arc and ray BY be point C. So we have got this BC equal to 6.5 centimeters. Now next step would be join AC. So we have joined AC and in joining AC we obtain the triangle ABC. So thus we obtain triangle ABC in which we have AB equal to 4.5 centimeters. BC equal to 6.5 centimeters and angle ABC is equal to 60 degrees. Now next we need to construct a triangle similar to the triangle ABC whose sides are three fourth of the corresponding sides of the triangle ABC. Now next step is construct an acute angle Bax at A on the opposite side of vertex of triangle ABC. So we have constructed this acute angle Bax. Now since we need to construct a triangle similar to the triangle ABC with sides three fourth of the corresponding sides of triangle ABC. Now out of 3 and 4 in this fraction 3 upon 4, 4 is greater than 3. So in the next step we have locate four points A1, A2, A3, A4 on AX. So that we have A1 is equal to A1, A2 is equal to A2, A3 is equal to A3, A4. So here we have the points A1, A2, A3 and A4 such that A A1 is equal to A1, A2 is equal to A2, A3 is equal to A3, A4. Next we join A4B, so we have joined A4B. Now in the next step we have draw a line through A3 since 3 is smaller of the 2, 3 and 4. So we will take A3 and through the point A3 we will draw a line parallel to A4B so we have drawn a line through A3 which is parallel to A4B. This line through A3 intersects AB at point B dash so we have A3B dash is parallel to A4B. Then in the next step we draw a line through B dash parallel to BC. So through B dash we have drawn a line parallel to BC such that this line intersects AC at point C dash. So we have B dash C dash is parallel to BC. So this triangle AB dash C dash is the required triangle. Thus we have triangle AB dash C dash is the required triangle. Thus we have AC dash upon AC is equal to AB dash upon AB is equal to B dash C dash upon BC is equal to 3 upon 4. So this completes our construction. Hope you have understood the solution of this question.