indirect proof
given: plane M and N intersect; line CD is parallel to plane M; line CD is parallel to plane N; line CD and line AB are not skew
prove: line CD is parallel to line AB
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To prove that line CD is parallel to line AB, we can use an indirect proof.
Here's the step-by-step explanation on how to construct an indirect proof for this problem:
1. Assume for the sake of contradiction that line CD is not parallel to line AB.
2. Since line CD is parallel to plane M and line AB is not skew with line CD, it must intersect plane M.
3. Similarly, since line CD is parallel to plane N and line AB is not skew with line CD, it must intersect plane N.
4. Therefore, line AB intersects both plane M and plane N.
5. However, this leads to a contradiction, as we were given that plane M and plane N intersect at a point.
6. Hence, our assumption that line CD is not parallel to line AB is false.
7. Therefore, we can conclude that line CD is parallel to line AB.
By proving the contradiction to our initial assumption, we have demonstrated that line CD is indeed parallel to line AB.