Question

Solve 12 in copy......

Answer 1

$here \: is \: the \: answer \: of \: your \: question$

Given :- P and Q are points of trisection of diagonal BD of parallelogram ABCD.

To Prove :- CQ ll AP

Construction :- Join AP, AC and AQ, CQ

Proof :- As ABCD is a parallelogram and AC & BD are the diagonals which bisect each other at point O.

So, OA = OC

and OB = OD

Also, P and Q trisects the diagonal BD as given in question.

So, DQ = BP = PQ

Now, OB = OD

and BP = DQ

So, BP - OB = DQ - OD

OP = OQ.

Now, In quadrilateral APCQ. Diagonal AC and PQ bisect each other at point O such that OP = OQ and OA = OC.

So, APCQ is also a parallelogram. As it's diagonal bisect each other.

So, CQ ll AP


$hope \: it \: helps \: you$