Angle bisectors of a triangle; the incenter
- Two dots in one park — 3 tasks
- A distance to a fence, and two of them equal — 3 tasks
- Three bisectors, one point — 3 tasks
- The circle that touches all three sides — 3 tasks
- Going Deeper — 6 tasks
- Practice — 26 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.
-
The Same Distance From What? Incenter or Circumcenter — Cut & Glue Sort 20 minutes, including the cutting · 5 sheets
12 situations in words, sorted into the incenter, the circumcenter, or no single point. Walls, fences and streets are sides; gates, houses and "where the streets meet" are corners; and a thing the same distance from only two of them can go anywhere along one line.
-
How Far, and How Big? The Incenter — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a lettered triangle with its incenter or circumcenter: how far is the point from a side or a corner, or how big is an angle at the incenter? The wrong answers are the lesson's two mistakes — measuring to a corner or along a slanted segment, and using the whole angle where the half is needed. The row of box numbers at the foot is the check.
-
Is This Point the Incenter? — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each one scalene triangle with a dot and marks: small squares, ticks and arcs. Do the marks show that the dot is the incenter? Fill it or leave it white. Circumcenters, slanted segments that are not distances, and single angle bisectors are the white squares. When every square is right, a picture appears.
-
Half or Whole? Angles at the Incenter — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a scalene triangle with its incenter and the three segments from the corners. Halve an angle, double a part, find the angle at I, or halve the third angle. Using the whole angle where a part is needed lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.