Inscribed angles
- Four people look at one painting — 3 tasks
- Which arc the angle cuts off — 3 tasks
- One chord, twelve viewpoints — 3 tasks
- Why it comes out at half — 3 tasks
- Crossing the circle — 3 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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Inscribed and Central Angles: Half, Equal, or Neither? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a circle with its center, one marked angle and one thick arc. Students sort each piece: the angle is half the thick arc (an inscribed angle), equal to it (a central angle), or neither, because the thick arc is not the arc inside the angle. Obtuse inscribed angles and central angles marked the long way around are in every row.
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Inscribed Angles: Half the Arc — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with an inscribed angle. Some give the intercepted arc and ask for the angle; the others give the angle and ask for the arc. The wrong answers are the two commonest mistakes: copying the arc as the angle, and halving the angle when the arc is twice it. The row of box numbers at the foot is the check.
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Inscribed Angles: Are the Two Angles Congruent? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle with two marked angles. Students compute nothing: they find the arc inside each angle and decide whether the drawing shows the two angles congruent — the same arc, or arcs with the same measure. Vertices on opposite arcs, a central angle beside an inscribed one, and arcs nothing measures stay white. Fill it or leave it white, and a picture appears.
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Inscribed Angles: Half the Arc — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with an inscribed angle. Most give the central angle on the same two points and ask for the inscribed angle; on half of those the vertex sits on the short arc, so the angle is obtuse and opens onto the long arc. A few give the inscribed angle and ask for its arc. Copying the central angle, halving the wrong arc, or halving instead of doubling lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.