Answers:
- Segment XA and segment MC
- Point N
- Points A, N and X
- Plane ANC
- No, they are not coplanar
- Ray NM and ray NX
- Ray NM and ray NC
- Three lines
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Step-by-step explanation:
Problem 1
Technically there are no segments in this diagram because of the arrows that point in both directions for each line. However, you could make the argument that all you need to do is focus on two endpoints and that names a sub-segment of any given line. If this is what your teacher is going for, then two segments could be XA and MC
Something like "segment AC" isn't valid because there isn't a straight line connecting points A and C directly. So we can't pick any two points at random.
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Problem 2
Line CM and line RN intersect at point N
This point is on both lines simultaneously.
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Problem 3
Pick any three points that are on the same line. One such possible answer is Points A, N and X. They are all on the line XA.
Another possible answer would be points C, N and M.
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Problem 4
To name a plane, we can pick 3 points inside the plane that aren't collinear. One such possible answer is Plane ANC
We cannot label the plane as "plane ANX" because infinitely many planes pass through these collinear points. Think of the plane able to rotate like a propeller. So this is why we need 3 non-collinear points to uniquely define the plane.
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Problem 5
The points R, N, M and X are not in the same plane V. If we ignored point R, then the remaining points (N, M, X) are all in the same plane. However, the presence of R is what makes them not coplanar.
Think of points N, M and X being on the ground while point R is somewhere up in the air. Unfortunately the 2D diagram makes it tricky to show that R is above the plane.
So because those points are not in the same plane, we do not consider them coplanar.
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Problem 6
This is similar to problem 1. Technically there aren't any rays shown here, but we could focus on a subset of the line. Two possible answers are ray NM and ray NX
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Problem 7
Ray NM and ray NC can be glued together to form line CM. They point in completely opposite directions (eg: one points north, the other points south). Notice that rays NM and NC both start with the letter N to indicate that N is the endpoint (i.e. the part that doesn't go on forever).
Another possible answer would be ray NA and ray NX. They glue together to form line XA.
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Problem 8
There are 3 lines and they are:
To name a line, all we need are two points that are on the line itself. A line has a characteristic of going on forever in both directions. So that's why we have the double arrow symbol
overtop the line name.
Example:
