Pre-Calculus Homework Solutions 131

# Pre-Calculus Homework Solutions 131 - 16 A median of an...

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133 Chapter 5 10. Given: m ± / n Prove: Lines m and n intersect at exactly one point. Proof: Case 1: m and n intersect at more than one point. Step 1 Assume that m and n intersect at more than one point. Step 2 Lines m and n intersect at points P and Q . Both lines m and n contain P and Q . Step 3 By postulate, there is exactly one line through any two points. Thus the assumption is false, and lines m and n intersect in no more than one point. Case 2: m and n do not intersect. Step 1 Assume that m and n do not intersect. Step 2 If lines m and n do not intersect, then they are parallel. Step 3 This conclusion contradicts the given information. Therefore the assumption is false, and lines m and n intersect in at least one point. Combining the two cases, lines m and n intersect in no more than one point and no less than one point. So lines m and n intersect in exactly one point. 11. Given: n ABC is a right triangle; / C is a right angle.
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