Angles from chords, secants, and tangents
- Where the vertex sits — 3 tasks
- The exterior angle, both ways round — 3 tasks
- One triangle, a sum and a difference — 6 tasks
- When the second side is a tangent — 3 tasks
- Pushing the rules to their edges — 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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Angles from Chords & Tangents: Which Rule, and Is It Enough? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a circle with two chords crossing inside it or a tangent and a chord meeting on it, one marked angle, and some arc measures. Students sort each piece: half the sum (vertex inside), half the arc (vertex on the circle), or cannot tell, because an arc the angle needs has no number and 360° cannot find it.
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Angles from Chords, Secants & Tangents — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with two lines meeting inside, on, or outside it, and one marked angle. The wrong answers are the two commonest mistakes: forgetting to halve, and using half the difference where half the sum belongs (or the reverse). The row of box numbers at the foot is the check.
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Angles from Chords & Secants: Half the Sum? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle with two lines, one marked angle and two thick arcs, and no numbers. Students decide one thing: is the marked angle half the sum of the two thick arcs? Chords crossing with the right pair of arcs fill the square; the other pair at the same crossing, or two secants meeting outside the circle, stay white. Fill it or leave it white, and a picture appears.
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Angles from Chords, Secants & Tangents — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with two lines and one marked angle: two chords crossing inside the circle, a tangent and a chord meeting on it, or secants and tangents meeting outside it. Two arc measures are printed on every card. Forgetting to halve, mixing up half the sum and half the difference, or taking the arc on the wrong side of the chord lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.