Question

ABCD is a quadrilateral in which P,Q,R and S midpoint of the sides AB,BC,CD and DA respectively.If BD=12 cm Then the length of QR Is

Answer 1

Answer:

In the triangle, ΔACD, S and R are midpoints of AD and CD.

So, from Midpoint theorem, we can say that, SR∣∣AC and SR=12AC->(1)

Similarly, in the triangle, ΔACB, P and Q are midpoints of AB and CB.

So, from Midpoint theorem, we can say that,

PQ∣∣AC and PQ=12AC->(2)

From (1) and (2),

SR=PQ=12AC

Also, as both SR and PQ are parallel to AC, so, both of them should also be parallel to each other.

So, PQ=SRandPQ∣∣SR

Similarly, we can show that , SP∣∣RQandSP=RQ

Thus, PQRS is a parallelogram.

There goes your answer. Please mark me as branlist

Answer 2

Answer:

6cm

Step-by-step explanation:

just draw the diagram and join bd and qr

clearly by midpoint theorem , line segment qr is half of diagonal bd , because q and r are midpoints which if joined will be parallel to the third side of triangle bcd and follow all the properties of mid point theorem .

given bd = 12cm

=> bd/2 = 12/ 2 which is equal to qr

=>qr=6cm