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. ac and eg are coplanar.
7. plane abc intersects plane aj in ac.
8. ij intersects eg at point i.
9. planes egh and cdh intersect in point h.
10. planes egh and j intersect in point j.

Explanation:

Step1: Recall definitions

Coplanar points lie on same plane, collinear on same line. Analyze each statement with figure.

Step2: Evaluate statement 6

Points E, J, H are not on same line. False.

Step3: Evaluate statement 7

Points F and D are on same line. True.

Step4: Evaluate statement 8

Points A, F, B are on same plane. True.

Step5: Evaluate statement 9

Points A, F, H are on same plane. True.

Step6: Evaluate statement 10

Points A, C, D, H are on same plane. True.

Step7: Evaluate statement 11

\(\overrightarrow{AC}\) and \(\overrightarrow{EG}\) are not on same plane. False.

Step8: Evaluate statement 12

Plane ABC intersects plane AJ at line \(\overrightarrow{AC}\). True.

Step9: Evaluate statement 13

\(\overrightarrow{IJ}\) intersects \(\overrightarrow{EG}\) at point I. True.

Step10: Evaluate statement 14

Planes EGH and CDH intersect at point H. False, intersect at line \(\overrightarrow{DH}\).

Step11: Evaluate statement 15

Planes EGH and J intersect at point J. False, not clear what "J" represents as a plane.

Answer:

1. False
2. True
3. True
4. True
5. True
6. False
7. True
8. True
9. False (Intersect at line \(\overrightarrow{DH}\))
10. False (Unclear "J" as plane)