 Hi and how are you all doing today? The question says draw a triangle ABC with side BC equal to 7 centimeter angle B equal to 45 degrees and angle A equal to 105 degrees. Then construct a triangle whose sides are 4 by 3 times the corresponding sides of triangle ABC. Now here we will be doing the construction over here and we have already written down the steps of construction for you. The first step of construction is to draw a triangle ABC with BC equal to 7 centimeter angle B equal to 45 degrees and angle A equal to 105 degrees. So we have BC equal to 7 centimeter. Then we have angle B as 45 degrees. So using a protector or a compass you can draw a triangle, an angle of 45 degree at angle B. And now we have angle A as 105 degrees. So firstly we need to calculate what will be angle C. So we know that angle A plus angle B plus angle C is equal to 180 degrees. Angle A is 105 degrees, angle B is 45 degrees. So angle C will be equal to 30 degrees. So we need to draw an angle of 30 degree at C. So this point will be A. Right. Now the second step is to draw any rabiesx making an acute angle with BC on the side opposite to vertex A. Now we have a rabiesx which is opposite to the vertex A. We need to locate four points B1, B2, B3 and B4 on BX such that BB1 is equal to B1, B2 and so on. So let us locate four points. Let this be B1, B2, B3 and B4. Now next is to join B3 to C. Let us join B3 to C. Draw a line through B4 parallel to B3C intersecting the extended line segment BC at C dash. So let us erase this calculation first. What we need to do next is first of all we will be extending BC to a point Let us say D and now we will be drawing a line which is parallel to B3C through B4 which is intersecting the extended BC at C dash. Then we need to draw a line through C dash parallel to C A intersecting the extended line segment BA at A dash. So we have already have an extension of AB. Now through C dash we will be drawing a line which is parallel to AC intersecting the extended AB at A dash and A dash BC dash is our required triangle. So this A dash BC dash is the required triangle. Now for justification, we have triangle ABC similar to triangle A dash BC dash. So this implies that AB upon A dash B is equal to AC upon A dash C dash is equal to BC upon BC dash. But we know that BC upon BC dash is equal to BV3 upon BV4 which is equal to 3 upon 4 right. So therefore we can write the reciprocal of BC upon BC dash as BC dash upon BC will be equal to the reciprocal of 3 by 4 which is 4 by 3. So that clearly indicates that the reciprocal of this proportion that is A dash B upon AB is equal to A dash C dash upon AC is equal to BVC BC dash upon BC is equal to 4 by 3. So this is the required justification for the construction that we have done above. Hope you understood the construction well to make it very neatly and have a very nice day ahead.