 Hello friends, welcome to the session. I am Alka. Let's discuss the given position in figure 6.37 if triangle A,B,A,B is congruent to triangle A,C,D. Show that triangle A,D,E is similar to triangle A,B,C. Our given figure is a triangle A,B,C and we are given in the question that A,B,E is congruent to triangle A,C,B. And we have to show that triangle A,B,E is similar to triangle A,B,C. Let's begin with the solution. We are given triangle A,B,E is congruent to triangle A,B,A,C,B. We have to show that triangle A,B,E is similar to triangle A,B,C. So let's start with the proof. Since we are given the triangle A,B,E is congruent to triangle A,C,D. Therefore we can say that A,B equal to A,C by C,P,C,G. A,B equal to A,C. That is congruent part of congruent triangles are equal. So let this be our first equation. And we can also say that A,E equal to A,D again by C,P,C,T. Since the two triangles A,B,E is congruent to triangle A,C,B. Therefore A,B is equal to A,C since congruent part of congruent triangles are equal and A,E is equal to A,D by C,P,C,T. This can also be written as A,D equal to A,E. Select this we are second equation. Now on dividing first by second we get A,B upon A,D equal to A,C upon A,E. This can be written as A,B upon A,C equal to A,D upon A,E. Let this be our third equation. Now in triangle A,D,E and triangle A,B,C we have A,B upon A,C equal to A,D upon A,E from equation third. And we also have angle B,A,C equal to angle D,A,E that is a common angle in both the triangles. Therefore angle B,A,C equal to angle D,A,E common angle. Now therefore by SAS criteria of similarity. We all know that in SAS criteria if one angle of a triangle is equal to one angle of the other triangle and the sides including these angle are proportional then the two triangles are similar. And we can see here that one angle of a triangle is equal to the other angle of the triangle and the sides are also proportional then we can say that the two triangles are similar. Therefore triangle A,D,E is similar to triangle A,B,C. So this is proved that triangle A,D,E is similar to triangle A,B,C by SAS property. Now hope you understood the solution and enjoyed the session. Goodbye and take care.