Identify parallel lines

Detailed Explanation: Identify parallel lines

Parallel lines are lines that:

• lie in the same flat plane,
• always stay the same distance apart, and
• never meet, even if you extend them forever.

Line segments are parallel when they lie on parallel lines. Parallel segments point in the same direction. They may be horizontal, vertical, or slanted.

Example

Look at this rectangle with a diagonal:

A -------- B
| \        |
|   \      |
|     \    |
D -------- C

Which pairs of segments are parallel?

The segments shown are $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DA}$, and $\overline{AC}$.

Step 1: Look for segments with the same direction.

• $\overline{AB}$ and $\overline{CD}$ are both horizontal.
• $\overline{DA}$ and $\overline{BC}$ are both vertical.
• $\overline{AC}$ is slanted.

Step 2: Check that the segments do not meet when their lines are extended.

• The top and bottom lines through $\overline{AB}$ and $\overline{CD}$ stay the same distance apart, so they are parallel.
• The lines through $\overline{DA}$ and $\overline{BC}$ also stay the same distance apart, so they are parallel.

Step 3: Do not choose segments that intersect.

The diagonal $\overline{AC}$ meets the other sides at points $A$ and $C$, so it is not parallel to them. Also, adjacent sides such as $\overline{AB}$ and $\overline{BC}$ meet at $B$, so they are not parallel.

Therefore, the parallel pairs are

and

To identify parallel lines, first compare their directions, then make sure they will never intersect.