Alternate Angles on Parallel Lines

Alternate angles lie between two lines, on opposite sides of a transversal. This NSW Year 7 maths subtopic (NESA outcome MA4‑ANG‑C‑01) shows that they are equal whenever the two lines are parallel.

You will find alternate pairs by their Z shape, work out missing angles from diagrams and from named points such as \(\angle AXY\), and write a correct reason for each answer. Harder questions place a point between two parallel lines and ask for the angle there. The rails and a diagonal brace of a gate make the same shape. This subtopic is part of Year 7 Angles.