Question

abcd is a parallegrm AP bisects angle A and CQ bisects angle C P lies on CD and Q lies on AB AP is parallel CQ

Answer 1

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

Answer:

Draw ABCD parallelogram and bisect angle A and C, and join lines AP and QC. Prove as described.

Step-by-step explanation:

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)