Question

P and Q are the mid-points of the opposite sides AB and CD of a parallelogram
ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a
parallelogram.





Please don't prank​

Answer 1

Answer:

sorry idon't know.... sorry idon't know

Answer 2

$\large{\underline{\underline{Given→}}}$

P and Q are the mid-points of the opposite sides AB and CD of a parallelogram

ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a

parallelogram.

$\large{\underline{\underline{Solution→}}}$

According to the question, P is the midpoint of AB

Q is the midpoint of CD

Now,

AB||CD,

Also,

AP||QC

And, AB = DC

½ AB = ½ DC

AP = QC

Now, AP||QC and AP = QC

APCQ is a parallelogram.

AQ||PC or SQ||PR

Again, AB||DC means ½ AB = ½ DC

BP = QD

Now, BP||QD and BP = QD

BPDQ is a parallelogram.

So, PD||BQ or PS||QR

Thus, SQ||RP and PS||QR

${\boxed{\boxed{\rm{\pink{→\bar{PQRS \: is \: a \: parallelogram.}✔}}}}}$