 Hello friends, welcome to the session I am Alka, let's discuss triangles. Our given question is n figure 6.40 e is a point on side Cb produced of an isosceles triangle A,B,C with A,B equal to A,C. If A,D is perpendicular to B,C and EF is perpendicular to AC, we have to prove that triangle A,B,D is similar to triangle E,C,F. Let's start with the solution. We are given that triangle A,B,C is an isosceles triangle and we all know that in isosceles triangle two sides of the triangle are equal. We are given that the two sides A,B equal to AC. Now we are also given that A,D is perpendicular to B,C and EF is perpendicular to AC. Now we have to prove that triangle A,B,B is similar to triangle E,C,F. Now let's see the proof. Since we are given that A,B,C is an isosceles triangle, this implies that angle B equal to angle C. Since we know that angle opposite to equal sides of the triangle are equal. So we can say that angle B equal to angle C. Let this be our first equation. Now in triangle A,B,D triangle E,C,F we have angle A,B,B equal to angle E,C,F from equation first that is angle B equal to angle C, angle A,D,B equal to angle E,F,C equal to 90 degree. We are given that A,D is perpendicular to B,C and EF is perpendicular to AC. We are given. Now therefore by A,A criteria of similarity angle A,B,B is similar to triangle E,C,F. Let's prove that triangle A,B,D is similar to triangle E,C,F which was the required result. Hope you understood this solution and enjoyed the session. Goodbye and take care.