SOLUTION: point P is not on line AB. line BV and FG both run through P and line AB. what can you conclude about line BV and line FG. A. BV and FG cannot both be perpendicular to AB B.BV

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Question 1204564: point P is not on line AB. line BV and FG both run through P and line AB. what can you conclude about line BV and line FG.
A. BV and FG cannot both be perpendicular to AB
B.BV and FG are congruent lines
C. BV and FG are perpendicular to each other
D.BV and FG are both perpendicular to AB
E.BV and FG intersect AB at the same point
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Let's Assume That The Given Line is AB, and the point is P, which is not on AB.
Now, Let's assume, We have drawn a perpendicular BV on AB, and intersecting line AB at a point+O.
We have to prove that, this BV is the only line passing through P that is perpendicular+to AB.
Now, we will use a construction.


Let's construct another perpendicular+FG+on AB from point P.
Proof:
We have,
BV+perpendicular AB.
Also, FG perpendicular AB.
So, BV || FG. [Both are perpendiculars on the same line.]
Now since both BV and FG have point P+%7D%7Din+common+and+they+are+parallel%2C+means+they+should+%7B%7B%7Bcoincide.
So, BV and FG+are the coincident lines or parallel lines and only one of them passes through point aP}

answer:

A.BV and FG cannot both be perpendicular to AB

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The statement of the problem is not sufficient to get a single answer from among the answer choices.

Choice B makes no sense and so can't be a right answer; lines are infinite in length and can't be congruent.

Choice C is not right. You can certainly make BV and FG perpendicular, but that will be a very special case.

Now what about choices D and E....

If two lines are perpendicular to a given line and both pass through a point P not on that line, then the two lines are the same line, and they will intersect the line at the same point.

And there is nothing in the statement of the problem that says BV and FG can't be the same line.

So answer choices D and E are both possible in one special case, but they are not true in the general case.

And answer choice A is not true in the special case where BV and FG are the same line.

So, because the statement of the problem does not specify that BV and FG are not the same line, none of the conclusions A to E is possible.