Major confusion: '...is 1st line perpendicular to plane?'

[Mathgirl2011]

Hello,
I am working on my Geometry and stumbled across this one problem that has gotten me very confused. It reads:

" If a line is perpendicular to two intersecting lines in a plane, is the first line perpendicular to the plane? Why or why not?"

Now this may seem like a very simple problem to you, but I am completely stumped. I thought that the answer would be yes because if a line is perpendicular to ANY two intersecting lines then it has to be perpendicular to the plane. Am I completely hopeless? Please help!

 

[stapel]

Try working by contradiction:

Assume Lines A, B, and C are distinct and that they lie in the same plane. Let Line A be perpendicular to Lines B and C. Since Line A is perpendicular to Line B, then they meet at right angles. Since Line A is perpendicular to Line C, they also meet at right angles. By (some version of) the Alternate Interior Angles Theorem, this says that Lines B and C must be parallel.

But we are told that Lines B and C are intersecting! So our assumption that Line A is in the same plane as Lines B and C must have been in error.

Hope that helps!

Eliz.