Start here

A parallelogram is a four-sided shape with two pairs of parallel sides. It has equal opposite sides. Do equal opposite sides make a parallelogram?

This track follows the Class 9 topic 4-gons (Quadrilaterals). A 4-gon is a shape with four straight sides.

• Which claims force the name — some measurements prove it. Some do not.
• One diagonal, two triangles — the first proof.
• Both pairs equal — a strong test, proved with SSS (three matching sides).
• Three more ways in — one pair, halved diagonals, opposite angles.
• The midpoint theorem — half of a side, and parallel to it.
• Medians and the centroid — three corner-to-midpoint lines meet at one point.
• The midpoint 4-gon — joining the side midpoints always makes a parallelogram.
• Fold lines and half-turns — how the parallelogram family shares its symmetry.
• Tiling with any 4-gon — why any tile covers a floor.

A quick catch-up

These earlier ideas help. Open any to refresh it first.

• The five names — each has its own conditions.
• One thing assumed, the rest proved — the habit of proof.
• One agreement, three results — angles and parallel lines.
• The point exactly halfway — the midpoint.
• Corners at a point add to 360° — used for tiles.
• A half-turn can fit a shape onto itself — turning symmetry.