SOLUTION: 1. Let be five points, no three of which are collinear. How many lines contain two of these five points?
2.If no four of the five points are coplanar, how many planes contain t
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-> SOLUTION: 1. Let be five points, no three of which are collinear. How many lines contain two of these five points?
2.If no four of the five points are coplanar, how many planes contain t
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Question 1192149: 1. Let be five points, no three of which are collinear. How many lines contain two of these five points?
2.If no four of the five points are coplanar, how many planes contain three of the five points?
Hint: (for 1 and 2, list all the lines and the planes as sets)
3.Suppose you have n points, no three of which are collinear. How many lines contain two of these n points?
4.If no four of the n points are coplanar, how many planes contain three of the n points?
Hint: (for 3 and 4, generalize in a form of a formula)
5.Prove theorem 1.1.4. The steps in the proof are already given: you just have to supply the reasons for each step.
Theorem 1.1.4. If two lines intersect, then their union lies in exactly one plane.
Proof: Let and be two intersecting lines.
∩ is a point p.
contains a point q ≠ p.
There is a plane E, containing and q.
E contains ∪ .
No other plane contains ∪ . Answer by ikleyn(53937) (Show Source):
