 Hi and how are you all today? The question says in triangle A, B, C, angle A is acute. B, D and C, E are perpendicular on A, C and A, B respectively. Proof that A, B into A, E is equal to A, C into A, T. So here let us have a diagram to model this situation. Here we have a triangle A, B, C where A is an acute angle. Let it be angle 1. So let angle B, A, C that is angle A be equal to angle 1, angle B, D, A be angle 2 and angle C, E, A be angle 3. Now in this question we are given that in triangle A, B, C, B, D is perpendicular on A, C and C, E is perpendicular on A, B. We need to prove that A, B into A, E is equal to A, C into A, D. So let us start with our proof. Now in triangle A, D, B and triangle A, E, C we have angle 1 which is common to each other. Now next we can write that angle 2 is equal to angle 3 equal to 90 degree which is already given to us in the question and thirdly we have therefore triangle A, D, B similar to triangle A, E, C by A, A similarity. Now we know that when two triangles are similar then D, B upon E, C will be equal to A, B upon A, C will be equal to A, D upon A, E because in similar triangles the corresponding sides are proportional. So now taking this we can write that A, B upon A, C is equal to A, D upon A, E we have taken these two groups, on cross multiplying we have A, B into A, E equal to A, C into A, D and this is what was needed to be proved in this question. So hence we have proved the given question. Right, so this completes the session. Hope you understood the whole concept well and enjoyed it too. Have a nice day.