## Content description

Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)

Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)

### Elaborations

- defining and classifying pairs of angles as complementary, supplementary, adjacent and vertically opposite
- constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
- defining and identifying the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

### Points and lines in a plane

The following points describe some necessary ideas.

- A point either lies on a line or does not lie on a line.
- There is exactly one line passing through two distinct points.
- Two distinct lines in the plane either meet at a point or are parallel.
- Two lines in a plane are called
**parallel**if they never meet, no matter how far they are**produced**(meaning extended). This is written*AB*||*PG.* - Two lines parallel to a third line are parallel to each other.
- Three points that all lie on the one line are called
**collinear**. - Three lines that all pass through one point are called
**concurrent**.