Question

plz do it I can't get the answer​

Answer 1

Given :-

• ∠B = 90°

• P is a point on AC.
• ∠PBC = ∠PCB

To Prove :-

• PA = PB

Solution :-

Let ∠PBC and ∠PCB = x

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Now,

In ΔABC,

∠B = 90° , ∠C = x

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We know that in a Δ , sum of all angles is 180.

→ ∠A + ∠B + ∠C = 180°

→ ∠A + 90 + x = 180

→ ∠A = 180 - 90 - x

→ ∠A = 90 - x ------1

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∠ABP = ∠ABC - ∠PBC

∠ABP = 90 - x ----2

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.·. ∠ABC = ∠ABP ( From 1 & 2 )

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We know that in a Δ, sides opposite to equal angles are equal,

Therefore, PA = PB

Answer 2

SOLUTION:

Given,

ABC is a right angled ∆, right angled at B.

∠PBC = ∠PCB= x(say)

TPT: PA= PB

Proof:

In ∆ABC,

∠ABC= 90°

∠ACB= x

=)∠BAC= 180°- (90°+x)

=)∠BAC= 180°- 90 -x

=)∠BAC= 90°-x..............(1)

And,

∠ABP= ∠ABC - ∠PBC

∠ABP= 90° -x................(2)

Therefore,

In ∆ABP,

∠BAP = ∠ABP

Therefore,

PA= PB

[since in a ∆ sides opposite to equal angles are equal in length]

Hence, proved

Hope it helps ☺️