What does it mean that a segment is perpendicular to a plane?
See solution.
Practice makes perfect
We are asked to prove the following claim.
2
&Given:&& PQ⊥planeM
&Prove:&& PQis the shortest segment
& && fromP to planeM
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 plane M and draw the line through Q and this new point R.
Since PQ is perpendicular to plane M, it is perpendicular to any line in M.
In particular, it is perpendicular to line QR, so triangle â–ł PQR is right.
This means that we can use the Pythagorean Theorem.
PQ^2+QR^2=PR^2
Since QR^2 is positive, removing it from the left hand side gives us an inequality.
PQ^2
