Perpendicular bisectors of a triangle; the circumcenter
- Three tents, one water can — 3 tasks
- Two lines, one crossing — 3 tasks
- One point, three equal distances — 3 tasks
- Build it, and close it with a circle — 3 tasks
- One circle through three points — 6 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.
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Is P the Circumcenter? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 triangles, each with a point P and what is known about it (tick marks, perpendicular bisectors, printed lengths, printed angles), sorted into "P must be the circumcenter", "P cannot be" and "cannot tell". The last row holds two equal distances only, one perpendicular bisector only, and a point inside an acute triangle with nothing else.
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Where Is the Circumcenter, and How Far Away? — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a short question about a circumcenter: how far it is from a corner, or where it is. The wrong answers are the two mistakes this lesson exists to stop — taking the distance to a side (or x) instead of the distance to a corner, and putting the circumcenter inside every triangle. The row of box numbers at the foot is the check.
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Is the Dot the Same Distance From Every Corner? The Circumcenter — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a triangle and a dot with lines or segments marked: fill the square only if the marks show the dot is the same distance from all three corners (two perpendicular bisectors, or three equal segments to the corners). Lines through corners, lines that are not square, and equal segments to the sides stay white. When every square is right, a picture appears.
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Perpendicular Bisectors and the Circumcenter — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each asking a distance or a coordinate that the circumcenter decides: the distance to a corner when the distance to a side is also given, half the longest side of a right triangle, two equal distances written with x, and the middle of a horizontal side. Each card's common mistake lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.