Points, lines, intervals and angles

Geometry language and notation: points, lines, rays, intervals, collinear and concurrent lines, and naming angles with three letters.

The language of geometry

A point marks a position. Name it with a capital letter, such as $A$.
A line goes on forever in both directions, such as line $AB$.
A ray starts at a point and goes on forever in one direction, such as ray $AB$.
An interval (or segment) is part of a line with two end points, such as interval $AB$.

Points are collinear if they lie on the same line.
Lines are concurrent if they all pass through one point.
Parallel lines never meet: $AB \parallel CD$.
Perpendicular lines meet at $90^\circ$: $AB \perp CD$.

Naming angles

An angle is formed by two rays that meet at a vertex. We name it with three letters, with the vertex in the middle: $\angle ABC$ is the angle at $B$ between rays $BA$ and $BC$.

Example 1●

Rays $OP$ and $OQ$ meet at $O$. Name the angle in two ways.

$\angle POQ$ or $\angle QOP$

The vertex O goes in the middle; the outer letters can be either way round.

Example 2●●

Three lines all pass through point $X$. What word describes them?

They are concurrent.

Flashcards

Interval

Part of a line between two end points.

Ray

Starts at a point and goes forever in one direction.

Collinear

Points on the same straight line.

Concurrent

Three or more lines through one point.

Symbol $perp$

is perpendicular to

Practice

Which has exactly two end points?
Which names the angle with vertex $B$?
Points that lie on the same line are:
$AB \perp CD$ means:
Lines that all pass through one point are:
A ray $AB$:
How many different intervals can be drawn between $4$ points, no three collinear?
Which symbol means "is parallel to"?