Collinearity Examples

Name four collinear points. On which line do they lie?

When points are collinear, that means they're all on the same line. The only points that are all on the same line are A, C, D, and F, since they all lie on line m.

Name a pair of parallel lines and a pair of intersecting lines.

Parallel lines never cross, while intersecting lines will cross only at one point. Lines l and m are parallel since they don't cross (even when we extend their arrows). As for the intersecting lines, we have two choices: lines m and n intersect at C, and lines l and n intersect at E.

Give another name for . 

The only other name that works is . Note that the first letter must be C, since that's where the ray starts. The only other point in the same direction as D is point F.

How many segments can you form from the drawn lines and points? 

There are eight possible segments. Note that segments like AC and CA are identical, so we only count one of them: AC, AD, AF, CD, CF, DF, BE, and CE.