Question

PQRS is a Trapezium in which PQ ‖ SR. A and B are Mid points of PS and QR respectively. PB produced meet SR produced at C. Prove that :
i) AB ‖SR ii) AB= (PQ+SR) ​

Answer 1

Answer:

Solution

Given: In trapezium PQRS, PQ || SR, M is the midpoint of PS and MN || PQ.

To prove: N is the midpoint of QR.

Construction: Join QS.

Proof:

In

△

S

P

Q

Since, M is the mid-point of SP and MO || PQ.

Therefore, O is the mid-point of SQ.

(By Mid-point theorem)

Similarly, in

△

S

R

Q

,

Since, O is the mid-point of SQ and ON || SR

Therefore, N is the mid-point of QR.

(SR || PQ and MN || PQ )

(By Mid-point theorem)

hope it's helpful to you~~