Question

PQRS is a trapezium in which PQ is parallel to SR.The diagonals PR and QS intersect at T show that PT/QT = RT/ST​

Answer 1

Answer:

Given:PQ=

3

2

RS

⇒

RS

PQ

=

3

2

In △PQR and △RXS

∠SRX=∠QPX (alternate angles)

Also, ∠RSX=∠PQX (alternate angles)

∴△PQR≅△RXS by AA similarity theorem.

Hence,

ar(△RXS)

ar(△PQR)

=(

3

2

)

2

=

9

4