Question

use the figure to the right. determine whether each statement is true or false. if false, change the statement to make it true.

1. points e, j, and h are collinear.
2. points f and d are collinear.
3. points a, f, and b are coplanar.
4. points a, f, and h are coplanar.
5. points a, c, d, and h are coplanar.
6. (overrightarrow{ac}) and (overrightarrow{eg}) are coplanar.
7. plane abc intersects plane aij in (overrightarrow{ac}).
8. (overleftrightarrow{ij}) intersects (overrightarrow{eg}) at point i.
9. planes egh and cdh intersect in point h.
10. planes egh and j intersect in point j.

Explanation:

Step1: Check collinearity and coplanarity definitions

Use figure - check if points lie on same line (collinear) or same plane (coplanar), and intersection of planes/lines.

Step2: Analyze each statement

1. False, E, J, H not collinear. Change: Points E, J, D are collinear.
2. False, F, D not collinear. Change: Points F, B, D are collinear.
3. True.
4. True.
5. True.
6. True.
7. False, plane ABC intersects plane AIJ in line containing AC. Change: Plane ABC intersects plane AIJ in AC.
8. True.
9. True.
10. True.

Answer:

1. False, Points E, J, D are collinear.
2. False, Points F, B, D are collinear.
3. True
4. True
5. True
6. True
7. False, Plane ABC intersects plane AIJ in AC.
8. True
9. True
10. True