Question

6 ag is parallel to plane hkl. 7 gl and cd are parallel lines. 8 plane djk is parallel to plane abh. 9 fl and ic are skew lines. 10 de is skew to plane agf.

Explanation:

Step1: Recall parallel and skew - line/plane definitions

Parallel lines lie in the same plane and do not intersect. Skew lines are non - coplanar and do not intersect. A line is parallel to a plane if it does not intersect the plane. Two planes are parallel if they do not intersect.

Step2: Analyze statement 6

Line $\overleftrightarrow{AG}$ and plane $HKL$: By observing the 3 - D figure, we can see that $\overleftrightarrow{AG}$ does not intersect plane $HKL$, so $\overleftrightarrow{AG}$ is parallel to plane $HKL$. This statement is True.

Step3: Analyze statement 7

Lines $\overleftrightarrow{GL}$ and $\overleftrightarrow{CD}$: $\overleftrightarrow{GL}$ and $\overleftrightarrow{CD}$ are not in the same plane and do not intersect, so they are skew lines, not parallel lines. This statement is False.

Step4: Analyze statement 8

Planes $DJK$ and $ABH$: By observing the 3 - D figure, we can see that planes $DJK$ and $ABH$ do not intersect, so plane $DJK$ is parallel to plane $ABH$. This statement is True.

Step5: Analyze statement 9

Lines $\overleftrightarrow{FL}$ and $\overleftrightarrow{IC}$: $\overleftrightarrow{FL}$ and $\overleftrightarrow{IC}$ are not in the same plane and do not intersect, so they are skew lines. This statement is True.

Step6: Analyze statement 10

Line $\overleftrightarrow{DE}$ and plane $AGF$: $\overleftrightarrow{DE}$ is parallel to plane $AGF$ (it does not intersect the plane), not skew to it. This statement is False.

Answer:

1. True
2. False
3. True
4. True
5. False