how do you write out proofs?
To be more specific with my question, how do you find the alternate exterior angles theorem?

Be sure the result is not a postulate. If it is then there's nothing to prove, it's given. If it is a theorem -a provable statement- then review the avialable definitions, postulates and theorems to find a proof strategy. Generally, proving theorems is a trial and error process and you should improve in your ability to write them with practice.

ok so there is an isosceles triangle with altitude 'cd' and the left angle is 'a' and the right is 'b'. ok so if 'ad' is 4m and if 'db' is 9m then wat is 'cd' and how do u get it?

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