 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says triangle ABC is an isosceles triangle in which AB equals to AC. That is, AB is equal to AC. Sight BA is produced to D such that AD is equal to AB. That means AD is equal to AB is equal to AC. See the figure 7.34 that is this figure. Show that angle BCD is a right angle that means we have to show that this is a 90 degree angle. Let us start with a solution to this question. Let this be the angle 1, this be the angle 2, this be the angle 3 and this be the angle 4. Then we see that angle 1 is equal to angle 2 because angles opposite to equal sides are equal and AB is equal to AC that is given to us in the question. Since AB is equal to AC and AB is equal to AD then AC is equal to AD. Therefore again by this theorem we have angle 3 is equal to angle 4. Now in triangle BCD that is this triangle angle B plus angle C plus angle D is equal to 180 degree or angle 1 plus angle 2 plus angle 3 plus angle 4 is equal to 180 degree or twice of angle 2 plus twice of angle 3 is equal to 180 degree because angle 1 is equal to angle 2 if earlier proved and angle 3 is equal to angle 4. We can also say twice of angle 2 plus angle 3 is equal to 180 degree therefore angle 2 plus angle 3 is equal to 180 degree divided by 2 that is equal to 90 degree or we can say angle BCA plus angle DCA is equal to 90 degree or angle BCD is equal to 90 degree. Hence angle BCD is a right angle hence proved. So I hope you understood the question and enjoyed the session have a good day.