Question

Abcd is a parallelogram object ingale cq bisect angle c p lion cdn q lie on a b so that a parallel c q and a qcp is parallelogram

Answer 1

Answer:

Given that : ABCD is a parallelogram.

AP and CQ are bisector of angle A and C respectively.

Since opposite angles are equal in a parallelogram.

Therefore, ∠A = ∠C

 1/2∠A = 1/2∠C   

∠1 = ∠2

Now, ABIICD and the transversal CQ intersects them.

∠2 = ∠3 .

from these we get

∠1= ∠3

Thus, transversal AB intersects AP and CQ at A and Q such that ∠1= ∠3 i.e. corresponding angles are equal.

AP II CQ 

Answer 2

Given ABCD is a parallelogram.


As opposite angles are equal in a parallelogram;


∠A = ∠C


Again given, AP and CQ are bisector of angle A and C, respectively.


1/2∠A = 1/2∠C


∠APD = ∠QCD


Hence, AP II CQ (as corresponding angles are equal)



Also, in AQCP


As, AB II DC, so AQ II PC.


Also, AP II CQ.

So, AQCP is a parallelogram



(proved)