Question

ABCD is parallelogram AP bisect angle A and CQ bisect angle C. P lies on CD and Q lies on AB. so that -. (1)AP ll CQ. (2) AQCP is a parallelogram.
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Answer 1

Here is your answer:-

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

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 ll CQ ( as corresponding angles are equal ) ( part 1 proved )

Part 2:

Also, in AQCP

As, AB ll DC , so AQ ll PC

Also, AP ll CQ

So, AQCP is a parallelogram ( proved ).

Hope it helps uh.....

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