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6.3 - Copy

# 6.3 - Copy - 6-3 Theorems on Lines and Planes A Postulate...

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6-3 Theorems on Lines and Planes A) Postulate 4-7 review a. Postulate 4 (The Line Postulate) i. For every 2 points there is exactly one line that contains both points b. Postulate 5 i. Every plane contains at least three noncollinear points ii. Space contains at least four noncoplanar points c. Postulate 6 i. If two points of a line lie in a plane, then the line lies in the same plane d. Postulate 7 i. Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane B) Prove theorem 3-2 with an Indirect Proof

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a. Theorem 3-2 i. If a line intersects a plane not containing it, then the intersection contains only one point 1. ii. Hypothesis 1. L intersects E in at least one point P, and 2. E does not contain L a. Indirect Proof 3. Supposition- the intersection contains two points (Q also) a. i. Which one of our hypothesis get refuted b/c of our drawing? ii. Therefore, our supposition is false proving that theorem 3-2 is true C) Prove theorem 3-3 with an Indirect Proof a. Theorem 3-3 i. Given a line and a point not on the line, there is exactly 1
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