Points and lines are basic elements of planimetrics.

**Point** has no size (no width, no length, no depth) and is shown by a dot. It’s usually named with a capital letter.

**Line** is a collection of points arranged in a straight path that’s endless in both directions. Therefore it has one dimension: length.

A line can be identified in two ways: either by two points that are on the line, or by a lowercase letter. It has no ending on both sides.

This is line $AB$ or$\overleftrightarrow{AB}$

Also, we could call it line $a$.

**Ray** is a line that has an endpoint on one side and continues off to infinity on the other side. We can name a ray using its starting point and one other point that is on the ray, or we can use a lowercase letter.

This is ray $AB$, $\overrightarrow{AB}$, or simply ray $a$.

**Line segment** is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

This is line segment $AB$ or simply $\overline{AB}$.

There are $3$ tipes of line segment:

**closed line segment**– includes both endpoints**open line segment**– excludes both endpoints**half-open line segment**– includes only one endpoint (doesn’t matter which one)

### Relationships between a point and a line

- $A \in p$

There are two ways to read this: line $p$ goes through the point $A$ or point $A$ lies on the line $p$

- $A \notin p$

Meaning: line $p$ doesn’t go through the point $A$ or point $A$ doesn’t lie on the line $p$

- $p \bigcap q = {A}$

Meaning: lines $p$ and $q$ intersect on point $T$ or point $T$ is an intersection of lines $p$ and $q$.

- Points $A$ and $B$ lie on the same side of line $p$ from the point $C$

- $A$ and $B$ lie on the opposite sides of line $p$ from the point $C$, or point $C$ is between points $A$ and $B$

- Points $A$ and $B$ lie on the same side of line $p$

- $A$ and $B$ lie on the opposite sides of line $p$

$\Longrightarrow$ relationships between ray (line segment) and point are the same as above.

### Relationship between two lines

**Intersecting lines**A pair of lines are intersecting if they have a common point, also called as

**point of intersection**.

**$\quad$ Perpendicular lines**

A special type of intersecting lines where the angle of intersection is a right angle.**Parallel lines**Two lines are parallel if they lie in the same plane and do not intersect when extended on either side.

We say “*$p$ is parallel to $q$*” and write $p||q$.

**Euclid’s fifth postulate (parallel postulate) **

*“In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.”*

Note that the distance between two parallel lines is the same everywhere.

$\Longrightarrow$ relationships between ray (line segment) and point are the same as above.

## Line segments worksheets

**Constructing line segments** (173.2 KiB, 513 hits)

**Constructing angles** (118.4 KiB, 680 hits)

**Construction of angle bisectors** (438.2 KiB, 654 hits)

**Measuring lines in centimeters** (105.0 KiB, 725 hits)

**Measuring lines in millimeters** (73.8 KiB, 720 hits)