Question

1.1 practice a
in exercises 1 - 3, use the diagram.

1. name two points.
2. name two lines.
3. name the plane that contains point a, b, and e.

in exercises 4 - 7, use the diagram.

1. give one other name for $overline{mn}$.
2. name three points that are collinear.
3. name three points that are coplanar.
4. name a point that is not coplanar with points n, p, and t.

in exercises 8 - 10, sketch the figure described.

1. plane a and line c intersecting at all points on line c
2. $overline{gm}$ and $overline{gh}$
3. line $overline{cd}$ and plane x not intersecting

in exercises 11 - 14, use the diagram.

1. name a point that is coplanar with points a, d, and g.
2. name the intersection of plane heg and plane dfe.
3. name a point that is collinear with bh.
4. name a point that is not coplanar with points c, e, and m.
5. what geometric terms are modeled by the eiffel tower?

Explanation:

Step1: Identify points, lines and planes for 1 - 7

Based on the given diagrams.

1. For naming two points (Exercise 1), we can choose any two distinct points from the diagrams. For example, in the first - diagram, we can choose point A and point B.
2. For naming two lines (Exercise 2), in the first - diagram, we can name line AB and line CD.
3. For naming the plane containing A, B and E (Exercise 3), we look for the plane that passes through these three points.
4. For giving another name for $\overline{MN}$ (Exercise 4), we can use $\overline{NM}$ as the order of the endpoints of a line - segment can be reversed.
5. For naming three collinear points (Exercise 5), in the second - diagram, points M, N and P are collinear.
6. For naming three coplanar points (Exercise 6), in the second - diagram, points M, N and V are coplanar as they lie on the same plane A.
7. For naming a point not coplanar with N, P and T (Exercise 7), in the second - diagram, point W is not in the same plane as N, P and T.

Step2: Sketch figures for 8 - 10

1. To sketch plane A and line c intersecting at all points on line c (Exercise 8), we draw a plane and a line that lies entirely within the plane.
2. To sketch $\overline{GM}$ and $\overline{GH}$ (Exercise 9), we draw two line - segments with a common endpoint G.
3. To sketch line $\overline{CD}$ and plane X not intersecting (Exercise 10), we draw a line and a plane such that the line does not touch the plane.

Step3: Answer 11 - 14

1. For naming a point coplanar with A, D and G (Exercise 11), in the third - diagram, point B is coplanar with A, D and G as they all lie on the same face of the cube.
2. For naming the intersection of plane HEG and plane DFE (Exercise 12), in the third - diagram, the intersection is line EF.
3. For naming a point collinear with BH (Exercise 13), in the third - diagram, point M is collinear with BH.
4. For naming a point not coplanar with C, E and M (Exercise 14), in the third - diagram, point A is not coplanar with C, E and M.

Step4: Answer 15

The Eiffel Tower can be modeled by lines (the metal beams) and points (the joints where the beams meet).

Answer:

1. A, B
2. Line AB, Line CD
3. The plane passing through A, B and E
4. $\overline{NM}$
5. M, N, P
6. M, N, V
7. W
8. Sketch a line within a plane
9. Sketch two line - segments with common endpoint G
10. Sketch a non - intersecting line and plane
11. B
12. Line EF
13. M
14. A
15. Lines and points