Geometry / Mr. Hansen
11/30/2001

Name: _________________________

On my honor, I pledge that my work on this quiz is entirely my own, without use of book, Internet sites other than the Geometry Zone, notes, friends, parents, tutors, or anyone or anything else. In the event that I had advance knowledge of the contents of this quiz, I will have notified Mr. Hansen of that fact and will have arranged to take an "alternate alternate version." I understand that I am not required to report on my classmates by name, but that I must notify Mr. Hansen if I had any advance knowledge of the quiz, even if such knowledge was unintentional.

Signature: _____________________________ Start time: _____ End time: ______

Part I: Fill in the blank.

Your textbook listed five properties of lines and planes concerning || and ^ situations. (You can use these as theorems if you ever need them.)

5. If two distinct lines are ___________ to the same plane, then the ___________ are parallel.
6. If a plane is perpendicular to one of two parallel lines, then the plane is _____________ to the other line.
7. (Transitive property of || planes.) If two distinct _____________ are each _____________ to a third, then the first two are _____________ .
8. If a line is perpendicular to one of two parallel planes, then the line is _____________ to the other plane.
9. If two distinct planes are _____________ to the same line, then the _____________ are parallel.

10-13.

We say that line l is perpendicular to plane p, by definition, iff l is _____________ to every possible _____________ lying in p and passing through the _____________ . However, in practice, it suffices (by a theorem) to check that l is ^ to just _____________ distinct lines in p that cross at the foot.

14-16.

Non-intersecting, non-coplanar lines are called _____________ . Non-intersecting, coplanar lines are called _____________ . What are intersecting, non-coplanar lines called? _____________

Provide the diagram and fill in the reasons below to prove that if A and R lie in one plane, B and Q lie in a separate plane, segment AB is perpendicular to both planes, AB ¹ RQ, segments AB and RQ are coplanar, and ABQR is a quadrilateral, then ABQR is a trapezoid.

Important: Make a second diagram to show what situation is ruled out by the given fact that ABQR is a quadrilateral.

Diagrams (submit as a fax or a .JPG or .BMP attachment, or if you don't know how, just draw on a separate sheet of paper and bring to class on Monday, 12/3/01):

Provide a reason for each step below.

1. A and R lie in plane a, B and Q in plane b

2. segment AB ^ a, segment AB ^ b

3. a || b

4. segments AB and RQ lie in plane c

6. AB ¹ RQ

7. ABQR is a quadrilateral

8. ABQR is not a parallelogram

9. ABQR is a trapezoid