ABC is an isosceles triangle with AB = AC. Draw AP BC to show that ∠B = ∠C

Sure, here are the steps to prove that ∠B = ∠C in an isosceles triangle ABC with AB = AC and AP perpendicular to BC:

1. Draw triangle ABC such that AB = AC. This is given in the problem.

2. Draw a line segment AP such that it is perpendicular to BC. This means that ∠BAP and ∠CAP are right angles.

3. Now, we have two right-angled triangles, BAP and CAP.

4. In these triangles, AB = AC (given), AP = AP (common), and ∠BAP = ∠CAP (each 90 degrees).

5. Therefore, by the RHS (Right angle-Hypotenuse-Side) criterion of congruence, triangle BAP is congruent to triangle CAP.

6. This means that all corresponding parts of these congruent triangles are equal. Therefore, ∠B = ∠C.

So, we have proved that in an isosceles triangle ABC with AB = AC and AP perpendicular to BC, ∠B = ∠C.