Question

Bello chtars!
Math : Please be detailed​

Answer 1

Answer:

∆PTR ≅ ∆QTS,

By CPCT

PT = QT

TR = TS

PR = QS

∠PTR = ∠QTS

∠TRP = ∠TSQ

∠RPT = ∠SQT

Let,

a = ∠TRQ

b = ∠QSR

x = ∠PTQ

Thus,

In ∆TPQ

∠TPQ = ∠TQP = 90 [Angle Sum and Isoceles Triangle]

Similarly,

In ∆TRS,

∠TPQ = ∠TQP = 90 - x/2

[Angle Sum and Isoceles Triangle]

Similarly,

In ∆TRS,

∠TRS = ∠TSR = 90 - x/2

[Angle Sum and Isoceles Triangle]

Now,

90 - x/2 + 90 - [Angle sum in quadrilateral]

a = 90 - x/2 - y

Also,

90 - x/2 - y + b = 90 - [Angle S]

y = b

∠TQS = 90 - x/2

= 90 - x/2 - y + y [Adding and subtracting 'y']

= ∠QRT + ∠QSR [∠QRT = a, ∠QSR = b]

Therefore Proved