let me know if all of my answers are correct?...?

Question

1. 3 points are coplanar, they are collinear - TRUE
2. 2 lines intersect, they are coplanar - FALSE
3. 2 lines do not intersect, they are not on the same plane - TRUE
4. 3 planes intersect, their intersection is a point - FALSE
5. lines containing points M and N lies in one plane - FALSE
6. 3 points determine 3 distinct lines.
7. a point is between 2other points, then 3points are collinear-TRUe
8. 2 non-coplanar lines cannot intersect - FALSE
9. a line and a plane that do not intersect are paralleL - TRUE
10. 2 lines that do not intersect are skew - FALSE


tell me if my answers are correct and pls. "correct me if im wrong"

thank you so much...

Answer 1

1. Wrong. If three points lie in a plane, they are NOT necessarily on the same line.

2. Only correct in the case where the two lines are the same line. Otherwise false is incorrect.

3. Incorrect. Parallel lines don't intersect and they can be in the same plane.

4. Correct, they could be a line as well.

5. Correct.

6. False.

7. That depends on the meaning of between.

8. Incorrect. This is true. If they are not in the same plane, they cannot intersect since two intersecting lines determine a plane.

9. Correct.

10. Correct.

Answer 2

1. No, think of a triangle
2. No, they MUST be in a plane. Can you think of a counter-example?
3. No, parallel lines is the sole counter-example.
4. Yes, you are right. Their intersection could also be a line, or a plane if each plane is coplanar.
5. Yes, there is only one line connecting a given pair of non-super-imposed points. This line lies in an infinite number of planes.
6. Only if the three points are not colinear. If they are not colinear, they form a triangle, with exactly 3 sides.
7. Yes, assuming that the generally accepted definition of "between" is used. It is then simply a definition of coplanar.
8. No, any two intersecting lines define a plane. Therefore, from the contrapositive, (8) is true.
9. yes
10. yes

A good way to answer simple geometry problems like this is to just think about them. Try to find a counterexample to the statements, as I have done.

Answer 3

correct:3, 4, 7, 9
wrong:1- points in a triangle are coplanar but are not collinear. Hence, the answer is false.
2- true. Two lines are always coplanar,whether they intersect or not.
3- true.
5- true (reason mentioned above)
6- i dunno
Whats skew? if it is parallel, then your answer 10 is correct.

Answer 4

1) Not true because 3 points in c circle are coplanar not collinear
2) If 2lines intersect they have to be coplanar. So you are not right.
3) Again you are wrong because 2 lines may be parallel
4) You are right
5) You are right
6) False they may be collinear
7) your are right
8) You are wrong: They cannot intersect
9) you are right
10) you are right

Answer 5

No, fix #2, make it true.