Proving Properties of Quadrilaterals

This NSW Year 8 maths subtopic proves why parallelograms, rhombuses and rectangles have their properties: draw a diagonal, prove the two triangles congruent, then read the property off the matching parts. Stage 4 describes these properties; proving them is Stage 5 work in the NSW syllabus, so no Stage 4 outcome is given.

You will prove that a parallelogram’s opposite sides and angles are equal and that its diagonals cut each other in half, that a rhombus’s diagonals meet at right angles and halve its angles, and that a rectangle’s diagonals are equal. You will then use these properties with Pythagoras’ theorem and angle sums on a rhombus-shaped badge, a kite and a gate frame. It is part of Year 8 Congruent Figures.