 Hello and welcome to the session. I am Asha and I am going to help you with the following problem that says ABC is an isosceles triangle with AB is equal to AC, draw AP perpendicular on BC to show that angle B is equal to angle C. So this is the required figure of this problem and let us now begin with the solution. First we are given that ABC is an isosceles triangle so this is an isosceles triangle with side AB is equal to AC and we have drawn perpendicular AP on BC and we will show that angle B is equal to angle C. So we are given triangle ABC is an isosceles triangle with AB is equal to AC. We have drawn AP perpendicular on BC. After proofs angle B is equal to angle C. Now we just take triangles ABP triangle ACP these two triangles side AB is equal to AC which are the two hypotenuse in these two triangles. This is given to us an angle APB is equal to angle APC since they are right angles AP is perpendicular on BC this implies these two angles are of 90 degree each and also AP is equal to AP since these two sides are common. So this implies triangle ABP is concurrent to triangle ACP and this is that RHS rules congrats and this implies angle B is equal to angle C and this is that safety safety this is what we have to prove so angle B is equal to angle C and this completes the solution hope you enjoyed it take care and have a good day.