We are asked to prove the following claim.
2
&Given:&& AB⊥linep
&Prove:&& ABis the shortest segment
& && fromA to linep
This statement can be proven using either a direct or an indirect argument.
We show a direct proof here.
To start, let's add a point to the diagram on line p.
Since AB is perpendicular to line p, triangle â–ł ABC is right, so we can use the Pythagorean Theorem.
AB^2+BC^2=AC^2
Since BC^2 is positive, removing it from the left hand side gives us an inequality.
AB^2
