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Prove that if in Hilbert plane, the opposite angles of a quadrilateral are congruent, then the opposite sides are also congruent

I was able to do the reverse part, which is: "If in Hibert plane, the opposite sides of a quadrilateral are congruent, then the opposite angles are also congruent."
Could someone help me solve the main problem? Any guide I would be very appreciated! Thanks in advance

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  • $\begingroup$ I also proved that $2$ pairs of opposite sides must parallel $\endgroup$
    – Alex Nguyen
    Commented Jun 15 at 4:09
  • $\begingroup$ any idea? If Playfair axiom satified, I would be able to solve this problem. However, we just work in Hilbert plane (which means that Playfair axiom does not necessarily hold) $\endgroup$
    – Alex Nguyen
    Commented Jun 15 at 4:18

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