Perpendicular bisectors of chords
- Where is the centre of a broken plate — 3 tasks
- What one chord tells you — 3 tasks
- The perpendicular from the centre — 6 tasks
- The right triangle inside a circle — 3 tasks
- Going Deeper — 6 tasks
- Practice — 24 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.
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Perpendicular Bisectors of Chords: Do the Marks Prove It? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a circle with a chord, a line across it, some marks, and two thick arcs. Students sort each piece: the marks prove the thick arcs congruent, prove they are not, or cannot tell, because two diameters always cut each other in half and a square alone does not place the center.
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Perpendicular Bisectors of Chords: Radius, Half Chord and Distance — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with a chord, the perpendicular from the center to the chord, and a radius. Students use the right triangle of the radius, half the chord and the distance from the center to find a chord, a diameter or the distance. The wrong answers are the two commonest mistakes: giving half of what is asked, and giving the radius as the distance to the chord. The row of box numbers at the foot is the check.
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Perpendicular Bisectors of Chords: Do the Marks Prove It? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle with a chord and a line across it, some marks, and two thick arcs. Students compute nothing: they decide whether the marks prove the two thick arcs congruent — a line through the center perpendicular to the chord, a line through the center that cuts the chord in half, or the perpendicular bisector of the chord. Fill it or leave it white, and a picture appears.
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Perpendicular Bisectors of Chords: Radius, Half Chord and Distance — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with a chord, the perpendicular from the center to the chord, and a radius. Students use the right triangle of the radius, half the chord and the distance from the center to find a chord or a diameter. Giving half the chord for the chord, or the radius for the diameter, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.