CBSE Class 10 Maths (Basic) 2026 · Paper 430/3/1 · Question 33(b)

Triangles 5 marks Hard

In the given figure,

P QR S

is a trapezium with

P Q ∥ S R

. Diagonals

P R

and

QS

intersect each other at a point

T

. Prove that

\frac{P T}{T R} = \frac{QT}{T S}

. Further, if

T S = T R

, prove that

△ P T S \sim △ QT R

Part (b) : trapezium PQRS with PQ ∥ SR and diagonals meeting at T

Answer

Since

P Q ∥ S R

, the alternate angles give

△ P T Q \sim △ R T S

, so

\frac{P T}{T R} = \frac{QT}{T S}

. If further

T S = T R

, this forces

P T = QT

, and together with the vertically opposite angles

∠ P T S = ∠ QT R

it gives

△ P T S \sim △ QT R

by the SAS criterion. Hence proved in either alternative.

🔒 Step-by-step solution