I dontunderstand this question can you please help me. "Explain why 3 separate lines can all be parallel to each other,but 3 separate lines cannot all be perpendicular to each other. Use a drawing to show your answer."
three separate lines can be perpendicular, if you are considering three dimensional space, like on your table. One pencil laying on the table, a second pencil on the table perpendicular to the first, and a third pencil pointing straight up (not laying on the table, as you are holding it upwards.
So if you consider three lines in the same plane, as laying on your table, two of them can be perpendicular, but it is impossible to put a third pencil on the table perpendicular to both of the first two.
These are parallel lines:
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These are two perpendicular lines:
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Do you see why we can only have one pair of perpendicular lines?
Thank You very much
You're very welcome.
Sure, I can help you understand this question. Let's start by defining what it means for lines to be parallel or perpendicular.
When we say that lines are parallel, it means that they will never intersect each other, no matter how far they are extended. On the other hand, when lines are perpendicular, it means that they intersect at a right angle, forming a 90-degree angle.
Now, let's consider the first part of the question: why can three separate lines be parallel to each other? To answer this, we can look at a drawing.
Imagine drawing three parallel lines, such as railway tracks. No matter how far you extend them, they will never cross each other. This is because parallel lines maintain the same distance between each other at all points. So, it is possible for three separate lines to be parallel since they can have the same slope and never intersect.
Now, let's move on to the second part of the question: why can't three separate lines be perpendicular to each other? Again, we can use a drawing to illustrate this.
If you draw three lines that are perpendicular to each other, you will notice that they form a right angle at their intersection point. However, if you try to add a fourth line that is perpendicular to the other three, it won't be possible to maintain a right angle at all four intersections.
So, while two lines can be perpendicular to each other, it is not possible for three separate lines to all be perpendicular to each other simultaneously.
I hope this explanation helps you understand why three lines can be parallel to each other but cannot all be perpendicular to each other.