if line cd equal 2 and line xy equal 2, prove that line cd is equal to line xy
To prove that line CD is equal to line XY, we need to use the given information that line CD has a length of 2 and line XY also has a length of 2.
To do this, we can use a proof by contradiction. We will assume that line CD is not equal to line XY and then show that this leads to a contradiction.
Assume that line CD is not equal to line XY. This means that either line CD is shorter than line XY or line CD is longer than line XY.
Case 1: CD is shorter than XY
If line CD is shorter than line XY, then it must have a length less than 2. However, this contradicts the given information that line CD has a length of 2. Therefore, this case is not possible.
Case 2: CD is longer than XY
If line CD is longer than line XY, then it must have a length greater than 2. However, this also contradicts the given information that line CD has a length of 2. Therefore, this case is also not possible.
Since both cases lead to contradictions, our assumption that line CD is not equal to line XY must be false. Therefore, we can conclude that line CD is indeed equal to line XY.
In summary, by using a proof by contradiction, we have shown that line CD is equal to line XY based on the given information that both lines have a length of 2.