Question

Abcd is a square and p is the midpoint of ad. BP and cp are joined. Prove that angle PCB equals angle 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)

Answer 2

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