 Hello friends, welcome to the session. I am Malka. Let's discuss the given question CD and GH are respectively the biosecurs of angle A, C, B and angle EG, F such that E and G, D and H lie on sides AB and EF of triangle ABC and triangle EFG respectively. If triangle ABC is similar to triangle FEG, we have to show that CD upon GH equal to AC upon FG, triangle DCB is similar to triangle HGE and triangle DCA is similar to triangle HGF. On the basis of the vision we had figure ABC and FEG where CD and GH are biosecurs of angle C and G respectively and triangle ABC is similar to triangle FEG. Now let's begin with the solution. We are given that triangle ABC is similar to triangle FEG and we have also given that CD and GH are biosecurs of angle C and G respectively. Now let's begin with the proof. Now since we are given that triangle ABC is similar to triangle FEG, this implies that their corresponding angles are equal. So we can say that angle A is equal to angle and C equal to angle G since the given triangles are similar. Now let this be our first equation and now on dividing angle C and angle G by 2, dividing both sides by 2. We have 1 upon 2 angle C equal to half of angle G. This implies from the figure we can see that half of angle C is 1 and 2. So we can say that angle 1 equal to half of angle G which is 3 and 4. That is angle 1 equal to angle 3 and angle 2 equal to angle 4. Let this be our second equation. Since we are given that CD and GH are biosecurs of angle C and G therefore half of C equal to half of G. That is half of angle C and angle G respectively. Now since we have to show that the corresponding sides of the given triangle that is CD upon GH is equal to AC upon FG. For proving this part, we have to prove first of all that the two triangles, triangle DCA is similar to triangle HGF. So first of all let us prove the triangle DCA is similar to triangle HGF. So in triangle DCA by angle HGF we have angle A equal to angle F. This we had from our equation number 1 that angle A is equal to angle F, first equation. Then 2 equal to angle 4. This we had from our equation second here. From equation first and second we had that the two triangles are similar by AA criteria of similarity. Therefore by AA criteria of similarity DCA is similar to triangle HGF. Now we all know that in case of two similar triangles the ratio of their corresponding sides are equal. Therefore we can say that CD upon GH equal to AC upon FG which is the solution of first part and here we have already shown our third part. Now further let's see in triangle DCB and triangle HGE. We have 1 equal to angle 3 from our equation second as we have already shown it. And angle B equal to angle E. S triangle ABC is similar to triangle FEG we are given. Therefore by AA criteria of similarity we have triangle BCB similar to triangle HGE. Hope you understood the solution and enjoyed the session. Goodbye and take care.