Question

ABCD is a parallelogram. AP bisects ZA and CQ bisects ZC. P lies on CD and
lies on AB. Show that-
(1) AP||CQ
(ii
AQCP is a parallelogram.
Enr​

Answer 1

Answer:

Step-by-step explanation:

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)