Chapter 6.3, Problem 9CE

To determine

To find: the first sentence of an indirect proof of the statement shown.

Answer to Problem 9CE

“Assume temporarily that $l$ and $m$ are intersecting lines”.

Explanation of Solution

Given information:

Wishing to prove that $l$ and $m$ are skew lines, J began an indirect proof by supposing that $l$ and $m$ are intersecting lines.

Calculation:

The first sentence of his indirect proof was “Assume temporarily that $l$ and $m$ are intersecting lines.

Skew lines are lines that do not intersect and are not parallel.

They lie in different planes.

Start off an indirect proof by assuming temporarily that the given conclusion is incorrect. In this case, the correct sentence would be:

“Assume temporarily that $l$ and $m$ are not skew line”.

This covers the entire set of lines that are not skewed, which would be parallel lines,

Perpendicular lines and intersecting lines.

When J said “Assume temporarily that $l$ and $m$ are intersecting lines”, this does not cover parallel lines and perpendicular line.