ABCD is a square and P is the midpoint of AD BP and CP are joined Prove that - Maths - Triangles

Question

ABCD is a square and P is the midpoint of AD BP and CP are
joined Prove that angle PCB= angle PBC

Nakush · Accepted Answer

In triangle PAB and triangle PDC
AB = DC (sides of square)
angle A=angle D (each 90)
PA = PD (P is the mid point)
By SAS
triangle PAB is congruent to triangle PDC
PB = PC (By CPCT)
In triangle PBC
PB = PC (proved above)
angle PBC=anglePCB (angles opp to equal sides of a triangle are
equal)

ABCD is a square and P is the midpoint of AD. BP and CP are joined. Prove that angle PCB= angle PBC