Chapter 10.3, Problem 16Q

(a).

To determine

The two pair of parallel lines which lies in different plane.

Explanation of Solution

Given:

  

Solution:

In the given description,

i.e.,

  $k\parallel m\text{and}q\parallel p$

(b).

To determine

The two pair of perpendicular line.

Explanation of Solution

Given:

  

Solution:

In the given description,

  $k\perp n,m\perp n$ are the pair of lines perpendicular to each other.

(c).

To determine

The two pair of skew lines.

Explanation of Solution

Given:

  

Solution:

In the given description,

Line k, p and m, q are pair of skew lines.

(d).

To determine

To prove:

  $\angle 1\cong \angle 2$ .

Explanation of Solution

Given:

  

Proof:

In the given description,

  $\begin{array}{l}\angle 1\text{=}\angle 3\left(\text{vertically}\text{opposite}\text{angle}\right)\\ \angle 1\text{=}\angle 3=90°\end{array}$

Since,

Line k and m are parallel.

Therefore,

  $\angle 2\text{and}\angle 3$ are supplementary.

So,

  $\begin{array}{l}\angle 2\text{=}180°-90°\\ \angle 2\text{=}90°\end{array}$

Therefore,

  $\angle 1\cong \angle 2$