1. We need two points to define a line. A different way to say this is that if you have two points, you will need at least a line to hold them. In this sense, what do you need at least three points to define?
A. three lines
B. a ray
C. an angle or a plane
D. a line or an angle
E. a line segment
F. a point
2.
Two points define a line, but if there are two lines in a plane, and if they intersect somewhere, they “define” a single point. If there are two planes in space, and they intersect, what do they define? (Look at the walls of your room, where they meet. Imagine if there were no floor or ceiling, and the walls went up and down and side to side forever. What element describes where one wall meets another wall?)
A. a ray
B. a line
C. a point
D. a plane
E. a partridge
F. a pear tree
3.
Consider two lines that intersect in a single point in a plane. How many rays would it take to draw the same picture?
A. 3
B. 5
C. 1
D. 2
E. 6
F. 4
4.
Plane geometry as we study it now can be traced back to Euclid, and his book The Elements. Go HERE to find out more about that book. What does it mean when they say “A point is that which has no part.” Which of these best sums up that idea:
A. A point has no dimensions, it only defines a place in space
B. Points are only on lines, never by themselves
C. A point is only important if it defines a shape
D. Points are very big
E. Points are very small
F. Points stand alone and have nothing more to them
5.
Does every ray contain a line segment?
A. Only if there are three points on the ray
B. Yes, because all you need for a line segment is one point
C. No, because an element can’t be two things
D. No, because the end point is really an arrow
E. Yes, because every ray needs two points to define it
F. No because the points are busy making a ray
6. How many points are on a line?
A. No points
B. Exactly 1 point
C. Exactly 2 points
D. 5 or 6 depending on how long the line is
E. Infinitely many
F. We don’t know how many points are on a line.
7. Does every line contain a ray?
A. Yes, because a ray and a line both have arrows.
B. No, because the two points necessary for a ray are making a line
C. Yes, because a ray needs two points to exist, which are always part of a line.
D. Sometimes, if the arrows are in the right places
E. No, because lines don’t end and a ray needs an endpoint
F. Only if the line has three points on it
8.
Do two rays always define a plane?
A. No, because a ray can’t be used to define a plane
B. Yes, because we need three points
C. No, because two rays might only make one line
D. Yes, because rays can be extended into lines
E. No, because there aren’t enough points
F. Yes, because it’s the number of points that matter
9. If I have an angle between 10 and 170 degrees, do I have a plane?
A. Only if you have an additional point not on the angle
B. Yes, because a ray always defines a plane
C. No, because there aren’t enough points
D. Yes, because angles are big
E. No, because rays cannot be extended into lines
F. Yes, because that means you have two lines that meet at a single point
10. If I have a line, do I have a plane?
A. Only if you have an additional point not on the line
B. Only if you have an additional point that is on the line
C. Yes, because three collinear points define a plane
D. Yes, because a line has an infinite number of points
E. Only if the line has three points on it
F. Yes, because a line defines a plane
