Question

ABCD is a parallelogram. Prove that AC and PQ bisect each other.?

I'm clueless as I don't know how to solve this. I could use an explanation?

Answer 1

We can prove that `AC` and `PQ` bisect each other at `O` by proving that `△QOC` and `△POA` are congruent.

Firstly, identify corresponding points,

`△QOCharr△POA`
`color(white)(xxx..)QharrP`
`color(white)(xxx..)OharrO`
`color(white)(xxx..)CharrA`

`/_QCO=/_PAO` ( alternate angles )
`/_QOC=/_POA` ( vertically opposite angles )
`/_CQO=/_APO` ( alternate angles )

Hence, `△QOC-=△POA` and therefore, `AC` and `PQ` bisect each other.