Question

in fig. ABCD is a square and p is the mid point of AD. BP and CP are joined. prove that angle PCB=PBC

Answer 1

In triangle PBA and PCD
                 PA = PD (P is the mid point of AD)
                 Angle PAB = Angle PDC (90 degree)
                 AB = DC (two sides of square)
So triangle PBA congruent to PCD.
=> Angle ABP = PCD
Now if equals are subtracted from equals then the result is also equal.
                ABP +PBC=PCD + PCB
                         PBC=PCB (ABP and PCD canceled out as they are equal)