Chapter 6.3, Problem 11WE

To determine

To prove: that planes $P$ and $Q$ intersect.

Explanation of Solution

Given information:

  $\overleftrightarrow{AB}\cancel{\parallel }\overleftrightarrow{CD}$

Given figure,

  

Calculation:

An indirect proof is initiated by assuming temporarily that need to prove is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that $P$ and $Q$ do not intersect.

This means that they are parallel.

If this is the case, then the lines $\overline{AB}$ and $\overline{CD}$ in plane $N$ should be parallel to each other.

But this contradicts what is given i.e. $\overleftrightarrow{AB}\cancel{\parallel }\overleftrightarrow{CD}$ .

Hence, proved that $P$ and $Q$ intersect.