133Chapter 510. Given:m±/nProve:Lines mand nintersect at exactly one point.Proof:Case 1:m and n intersect at more than one point.Step 1Assume that mand nintersect at morethan one point.Step 2Lines mand nintersect at points Pand Q.Both lines mand ncontain P and Q.Step 3By postulate, there is exactly one linethrough any two points. Thus theassumption is false, and lines mand nintersect in no more than one point.Case 2:mand ndo not intersect.Step 1Assume that mand ndo not intersect.Step 2If lines mand ndo not intersect, thenthey are parallel.Step 3This conclusion contradicts the giveninformation. Therefore the assumption isfalse, and lines mand nintersect in atleast one point. Combining the two cases,lines mand nintersect in no more thanone point and no less than one point. Solines mand nintersect in exactly onepoint.11. Given:nABCis a right triangle;/Cis a rightangle.
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