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Answer 1

Step-by-step explanation

:In ∆PAB ans ∆PDC

AP = PD (as P is midpoint)

AB = DC ( all sides equal)

/_ A = /_ D (90°)

So∆PAB congruent to ∆PDC

So PB = PC by cpct

So ∆CPB is Isosceles Triangle and Opposite angles of Isosceles triangle is equal.

so /_ PCB = /_ PBCHence proved

Answer 2

Answer:

Step-by-step explanation:

ANSWER:-

P being a midpoint we can  divide the lines as:-

AP = PD

$\sf{In \ Triangle ABP \ and \ DCP}$

AB = DC [Sides of a square]

Angle ABP = Angle PDC [90 degree each]

PA=PD [ P midpoint , Proved Above]

By SAS Congruence,

Triangle PDC congruent to ABP.

Now, we can say that:-

PB = PC [CPCT]

And also we know that:-

If two sides of a triangle are same so the corresponding sides are also same.

So, Angle PBC = Angle PCB

More to Know:-

Types of Congruence:-

• ASA congruence:- In this the corresponding 2 angles and one side must be equal.
• SSS Congruence:- In this , three sides must be congruent
• RHS Congruence:- Hypotenuse and corresponding side (Base or height must be equal).