Inscribed angles on a diameter; inscribed polygons
- Where a paper corner fits — 3 tasks
- Diameter first, then the angle — 3 tasks
- From a right angle back to the diameter — 6 tasks
- A rectangle drawn inside a circle — 3 tasks
- Going Deeper — 7 tasks
- Practice — 27 tasks
- Summary — 2 tasks
- Cool-down — 6 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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Is It a Diameter? The Angle in a Semicircle — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a circle with lettered points, chords and some marks: the center, a right-angle square, an angle's measure, tick marks. Students sort each piece: the marks prove PQ is a diameter, prove it is not, or cannot tell. Angles that look right but are marked 84° or 96°, and chords that look like diameters with nothing to prove it, are the traps.
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The Angle in a Semicircle, Both Ways: Inscribed Angles on a Diameter — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. In some, the center is marked on a chord and students find an angle of the triangle drawn on that diameter. In others, a right triangle sits in a circle and students find the radius from the two legs. The wrong answers are the common mistakes: leaving out the right angle, and giving the diameter, or half a leg, as the radius. The row of box numbers at the foot is the check.
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Inscribed Polygons: Is Every Corner on the Circle? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle and a polygon. Students compute nothing: they check whether every corner of the polygon is on the circle. Near misses are the white squares: one corner just inside, one corner outside, and a circle sitting inside a polygon. Fill it or leave it white, and a picture appears.
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The Angle in a Semicircle, Both Ways: Inscribed Angles on a Diameter — Scavenger Hunt a full class period · 13 sheets
16 cards around the room. On some, the center is marked on a chord, so it is a diameter, and students find an angle of the triangle drawn on it. On others, a right triangle sits in a circle with no center shown, and students find the radius from the two legs. Leaving out the right angle, or giving the diameter as the radius, lands on a card that sends the group back. A clean run is 8 lines.