Multi-step and overlapping-triangle proofs
- Warm-up — 3 tasks
- Bridge — 3 tasks
- The part that is in both triangles — 3 tasks
- Using the first congruence — 3 tasks
- Going Deeper — 5 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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What Do the Two Triangles Share? Overlapping Triangles — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each two triangles drawn on top of each other, sorted into: they share a side, they share an angle but no side, or they share nothing. The last row holds what only looks shared: vertical angles where two triangles cross, a corner in common with different angles, and an overlap on one line.
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One Figure, Two Congruences — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, all about one figure of two overlapping triangles. The route walks a proof that needs two congruences, one step per box. The wrong answers are the two mistakes this lesson exists to stop: reading the figure wrongly (a shared angle missed, vertical angles taken as one angle, a length read off the drawing), and stopping after the first congruence. The row of box numbers at the foot is the check.
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Is It in Both Triangles? Overlapping Triangles — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each two triangles drawn on top of each other with one part marked: is that segment a side of both triangles, or that angle an angle of both? Fill or leave white. The white squares are the usual mistakes: the diagonal that crosses the shared side, an angle made of two angles, vertical angles taken as one shared angle. When every square is right, a letter appears.