## 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.