How do you write a proof for the following conditional? (Geometry)

Question

I am having trouble writing a proof for the two conditionals below. I was wondering how I would go about writing the ones below.

If two lines are perpendicular, then they form a 90 degree angle.

If two lines form a 90 degree angle, then they are perpendicular.

Thanks.

Answer 1

So, I think this problem is hard because the statements are obvious, and don't seem to need proof!
In a two column proof, I would use two statements other than given.

Given: lines l and m are perpendicular. Prove: Lines l and m form a 90 degree angle.
Statement                                                    Reason
1. Lines l and m are perpendicular                1. Given
2. Lines l and m form a right angle               2. Definition of perpendicular
3. Lines l and m form a 90^o angle                 3. Definition of a right angle

To prove the converse, just work backwards: if two lines form a 90 degree angle, then they form a right angle, by definition of a right angle. Since the lines form a right angle, they are perpendicular, by the definition of perpendicular.

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(Note: Hopefully your book definition of perpendicular says "two lines are perpendicular if they meet at a right angle" because the definition of "perpendicular" can vary a bit from text to text!)