Question

ABCD is a parallelogram.AP bisects angle A and CQ bisects angle c. P lies on CD and Q lies on AB . show that-
1) AP parallel CQ
2) AQCP is a parallelogram

Answer 1

i will hope that it will helps you

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:

Part 1:

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) (Part 1 proved)

Part 2:

Also, in AQCP

As, AB II DC, so AQ II PC.

Also, AP II CQ.

So, AQCP is a parallelogram (proved)