Question

In the trapezium PQRS, if the midpoints of the two non-parallel sides PS and QR are X and Y respectively then XY= )​

Answer 1

Answer:

Step-by-step explanation:

Given :- X and Y are respectively the mid points of non parallel sides PS and QR of a trapezium PQRS. Prove that XY parallel PQ and XY = 1/2(PQ + RS) .

Solution :-

Construction: Join QY and produce it to meet RS produced at T.

Now, in ∆PQY and ∆STY we have,  

PY = YS (Y is Mid - Point of PS.)

∠PYQ = ∠TYS (Vertically opposite angles.)

∠QPY = ∠YST (Alternate angles.)

So,

∆PQY ≅ ∆STY (BC ASA.)

Therefore,

PQ = ST (By CPCT.)

QY = YT (By CPCT.)

Now, in ∆QRT we have,

X is the midpoint of QR.

Y is the midpoint of QT

Therefore,

XY ∥ RT and,

XY = (1/2)RT (By Mid - Point theorem.)

Hence,

→ XY = (1/2)[RS + ST]

→ XY = (1/2)[RS + PQ]

→ XY = (1/2)[PQ + RS] .