Why can't we prove Euclid's fifth postulate from propositions 27 and 29?

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Proposition 29 state that:

A straight line falling on two parallel straight lines, makes the alternate angles equal to one another [...]

And the fifth postulate was used:

[...] therefore two straight lines which intersect are parallel to the same straight line, which is impossible.

Would a better postulate be, (distinct) lines parallel to the same line are parallel, and thus black and yellow are parallel, but they intersect, which is absurd, as it contradicts with the definition of parallel?