Montessori Geometry: Positions of a Single Line and Relationships Between Two Lines (Lesson and Quiz)

Learn about the positions of a single line (horizontal, vertical, and oblique) and relationships between two lines (parallel, intersecting, convergent, divergent, oblique, and perpendicular) as inspired by the Montessori geometry curriculum.

Positions of a Single Line

This is a line.

It extends in all directions.

This is a picture of the horizon.

The horizon is the line where the earth or the water seems to meet the sky.

If a straight line runs across from left to right — just like the horizon — it is called a horizontal line.

If a line goes straight from top to bottom, it is called a vertical line.

If a straight line is neither horizontal nor vertical, it is called an oblique line.

But that’s for one line.

What if we have two lines?

Remember that lines extend infinitely in both directions.

If two lines are beside each other but are always the same distance apart — no matter how much we extend them in both directions — and never, ever meet, they are called parallel lines.

Look around you and see if you can spot lines that are parallel to each other.

Parallel lines never meet. But lines that are not parallel do meet.

Lines that meet at one point are called intersecting lines.

Lines that are already growing apart, with the distance between them becoming greater and greater, are called divergent lines.

Lines that are still approaching each other, becoming closer and closer, are called convergent lines.

Now let’s see the ways that two straight lines can meet or intersect.

Two straight lines can meet this way:

OR

Two straight lines can meet this way:

Measure the angles in the first pair of lines.

None are right angles.

Now, measure the angles in the second pair of lines.

All are right angles.

When two straight lines meet and do not form right angles, the two straight lines are oblique to each other. Oblique means having a slanting direction or position.

When two straight lines meet and form all right angles, they are perpendicular to each other. Perpendicular means being at right angles to a line or surface.

Summary

Positions of a straight line:

The position of a single line can be either horizontal, vertical, or oblique (slanted).

Positions of two straight lines relative to each other (relationships between lines):

Lines that are always the same distance apart and never meet are called parallel lines.

Lines that meet at one point are called intersecting lines.

Lines that are still approaching each other are called convergent lines.

Lines that are already moving away from each other are called divergent lines.

Intersecting lines can be either oblique or perpendicular.

Lines that are oblique to each other are lines that meet but do not form right angles.

Perpendicular lines are two straight lines that meet — or intersect — each other at right angles.

Note about oblique lines:

A single oblique line is a line that is neither horizontal nor vertical.

Lines that are oblique to each other are lines that are neither parallel nor perpendicular.

Ready to test your knowledge on the positions of straight lines and the relations between two straight lines?

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