Cyclic quadrilaterals
- Where the fourth corner has to go — 3 tasks
- Two arcs that make the whole rim — 3 tasks
- Opposite corners, the whole rim — 6 tasks
- Reading it backwards — 3 tasks
- The diagonals, and proving the converse — 7 tasks
- Practice — 27 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
-
Cyclic Quadrilaterals: Do the Four Corners Lie on One Circle? The Converse — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 quadrilaterals drawn to scale with no circle and some angles printed. Students sort each piece: the four corners lie on one circle, they do not, or the numbers cannot tell. Opposite angles that add to 180° mean yes; an exterior angle or an angle cut in two by a diagonal must be worked out first; and two angles next to each other decide nothing.
-
Cyclic Quadrilaterals: Opposite Angles and Exterior Angles — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with an irregular quadrilateral whose four corners are on it. Students find the angle with the dashed arc: across from a given angle, from two angles next to each other, from an exterior angle, or from an angle cut in two by a diagonal. The wrong answers are the two commonest mistakes: taking opposite angles as equal, and using an angle next to the dashed one. The row of box numbers at the foot is the check.
-
Cyclic Quadrilaterals: Must Opposite Angles Add to 180°? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle and a shape with two angles marked and no numbers. Students compute nothing: they decide whether the two marked angles must add to 180°. That needs four corners, all on the circle, and whole angles at opposite corners. A corner off the circle, two angles next to each other, part of an angle, or a pentagon leaves the square white, and a picture appears.
-
Cyclic Quadrilaterals: Opposite Angles and Exterior Angles — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with an irregular quadrilateral whose four corners are on it. Students find the angle with the dashed arc: the angle across from a given one, from two angles next to each other, from an exterior angle, or from an angle cut into two parts by a diagonal. Taking opposite angles as equal, or using the wrong corner, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.