SOLUTION: Can you please help me with these problems? TRUE or FALSE. If the statement is not always true , then answer FALSE. 1. Through a given point not in a plane m, there is one and

Question 300571: Can you please help me with these problems?
TRUE or FALSE. If the statement is not always true , then answer FALSE.
1. Through a given point not in a plane m, there is one and only one line parallel to m.
2. Through a given point on a line, there is one and only one line perpendicular to the given line.
3. Through a given point on a line, there is one and only one plane perpendicular to the given line.
4. If a line is parallel to a plane, it is parallel to every line in the plane.
5. The altitude from the vertex of an isoceles triangle is also a median of the triangle.
Thanks!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
1. False. Imagine a spinner held above a table. The table would be the plane m while the spinner (which isn't in the plane) can point in any direction but still be parallel to the plane m. So there isn't a unique line that goes the given point (the center of the spinner).

2. True (assuming we're working in one plane, eg the 2D cartesian coordinate system). This can be shown algebraically.

3. True. Again, this can be shown algebraically.

4. False. It is possible to draw a line that lies in the plane, but that is not parallel to the given line.

5. True. The altitude bisects the base side.
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