 Let us discuss the following question. The question says, proof had in the right angle triangle, the square of the hypotenuse is equal to some of the squares of the other two sides. Using the above, proof the following. In triangle A, B, C angle A is equal to 90 degree and A, D is perpendicular to B, C. Proof had A, B squared plus C, D squared is equal to B, D squared plus A, C squared. Now, we will first prove the first part. This is the triangle given to us, which is right angle at D. A, C squared is equal to AB squared plus BC squared. Now, in construction, B, D perpendicular to AC. Let's now begin with the proof. A, D, B, A, D, B, both are equal to 90 degree. The common angle between these two triangles, AB, is similar to triangle ABC of similarity. D by AB is equal to AB by AC, because corresponding sides of similar triangles are proportional, and this equation is equation number five. B, D, C is similar to triangle ABC. These triangles are similar, therefore, their corresponding sides are proportional, and thus, we have BC by equation as equation number 80 is perpendicular to AC squared plus BT squared. Now, the given information, 90 degree, the CD squared is equal to AB squared. Let us name this as equation number two. Now, from plus BT squared. So this completes the session.