In English, the use of articles ('a,' 'an,' and 'the') is important to convey the correct meaning. The articles need to match the sounds that follow them (vowel or consonant sounds) and reflect definite or indefinite references.
Here is how the sentences should be corrected:
The old woman met a young man. (This sentence is already corrected).
The aeroplane flew into the sky.
'The sky' is something specific and unique, so we use 'the' as the article.
He travelled around the world.
'The world' refers to our planet Earth, which is a unique and singular entity, so the definite article 'the' is appropriate.
He is as brave as a lion.
This expression uses a comparison with 'a lion' in a generic sense to convey courage.
She is as wise as an owl.
'Owl' starts with a vowel sound, so we use 'an' instead of 'a.'
These corrections ensure that the sentences are grammatically correct and the articles are appropriately used.