Geometry

Lesson

We have seen a number of definitions and introduced quite a bit of new language in Geometry so far. Let us revise what we know and practise this a little before moving on to some new work.

**Line**: passes through two points and extends to infinity in both directions, notated

**Line segment**: starts at a point and ends at a point, notated

**Ray**: starts at a point and extends through a second point to infinity, notated

Angles

**Acute**: an angle measuring between $0^\circ$0° and $90^\circ$90°

**Right**: an angle measuring exactly $90^\circ$90°

**Obtuse**: an angle measuring between $90^\circ$90° and $180^\circ$180°

**Straight**: an angle measuring exactly $180^\circ$180°

**Reflex**: an angle measuring between $180^\circ$180° and $360^\circ$360°

**Revolution**: an angle measuring exactly $360^\circ$360°

Labelling angles

An angle is made by two lines joining at an APEX. We label an angle by moving from a point on one line (line, segment or ray), through the APEX to a point on the the other line (line, segment or ray).

Angle rules and definitions

**Angles at a Point**: Angles at a point sum to $360^\circ$360°

**Angles on a line**: Adjacent angles on a straight line are supplementary (add up to $180^\circ$180°)

**Supplementary Angles**: Sum to $180^\circ$180°

**Complementary Angles:** Sum to $90^\circ$90°

Vertically Opposite Angles

**Vertically opposite angles are equal. **

*(To help remember this, it is sometimes referred to as the X rule). *

In the following, state the vertex and name the angle.

Is the angle acute, obtuse or reflex?