The triangle midsegment theorem and its applications
- Three shapes, one fraction — 3 tasks
- Where the midpoints go, and what follows — 3 tasks
- Why the half never moves — 3 tasks
- Long or short, before any number — 3 tasks
- Going Deeper — 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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Halve It, Double It, or Can You Not Tell? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 triangles, each with a number on one segment and a question mark on another. Students do not work anything out: they decide whether the midsegment theorem says to halve the number, to double it, or says nothing at all. The last row holds the mistakes that matter: a midsegment paired with a side it touches, and a segment that only looks like a midsegment.
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Did You Find the Length, or Just x? Midsegments — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, all about one triangle with its three midsegments. Half the boxes give a midsegment or a side and ask for the other; half give both as expressions in x and ask for a length. The wrong answers are the two costliest mistakes on this topic: halving where doubling is needed (or the reverse), and handing in x instead of the length. The row of box numbers at the foot is the check.
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Is It Really a Midsegment? — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a triangle with one segment inside it, drawn or described: fill the square if the segment is a midsegment, leave it white if it is not. The white squares are the mistakes students really make: a median taken for a midsegment, a segment that is half as long as a side but does not join two midpoints, and tick marks read wrongly. When every square is right, a picture appears.
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Which Side Is the Midsegment Half Of? — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each one tilted triangle with one midsegment. Half the cards give the midsegment and ask for the side it does not touch; half give two sides and ask for the midsegment. Halving where doubling is needed, or halving a side the midsegment touches, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.