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EVEN MORE WELCOME ARE ANSWERS FROM FELLOW STUDENTS. BLOG ON!
Two lines perpendicular to the same line are _________(always/sometimes/never) parallel.
Many of you answered "always"... however, the correct answer was "sometimes"... here's why:
BY DEFINITION (in your BIBLE, of course... are you reading your Bible before you go to bed each night?) parallel line are coplanar, as are intersecting lines, btw. So, if two lines are perpendicular to the same line, they can be noncoplanar. Picture a line, m, formed by the intersection of two planes, horizontal plane A and vertical plane B. A horizontal line, a, in Plane A can be perpendicular to line m AND a vertical line, b, in plane B can be perpendicular to line m however line a and line b are clearly not parallel to one another.
If the statement had been: Two COPLANAR lines perpendicular to the same line are _________(always/sometimes/never) parallel.
... the answer would have been "always."
N.B. Also recall, when the book or I state "two lines" the assumption is that we are specifying two distinct/separate lines, so "two lines" (for the purpose of this course) will NEVER mean the same line.
im confused abut how you can tell if something is inductive or deductive
ReplyDeleteRe-read pgs 45 & 106 in the textbook... can you give a specific example?
ReplyDeleteProblem #16 from our Unit 1-3 "Booster" was:
ReplyDeleteTwo lines perpendicular to the same line are _________(always/sometimes/never) parallel.
Many of you answered "always"... however, the correct answer was "sometimes"... here's why:
BY DEFINITION (in your BIBLE, of course... are you reading your Bible before you go to bed each night?) parallel line are coplanar, as are intersecting lines, btw. So, if two lines are perpendicular to the same line, they can be noncoplanar. Picture a line, m, formed by the intersection of two planes, horizontal plane A and vertical plane B. A horizontal line, a, in Plane A can be perpendicular to line m AND a vertical line, b, in plane B can be perpendicular to line m however line a and line b are clearly not parallel to one another.
If the statement had been:
Two COPLANAR lines perpendicular to the same line are _________(always/sometimes/never) parallel.
... the answer would have been "always."
N.B. Also recall, when the book or I state "two lines" the assumption is that we are specifying two distinct/separate lines, so "two lines" (for the purpose of this course) will NEVER mean the same line.
Study Well,
Mr. C.