The converse; classifying triangles by side lengths
- Swapping the two halves of a claim — 3 tasks
- Two statements, one equation — 3 tasks
- Proving the converse — 3 tasks
- Why the comparison runs that way — 3 tasks
- Going Deeper — 6 tasks
- Practice — 26 tasks
- Summary — 6 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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Acute, Obtuse, or No Triangle at All? Classifying by Side Lengths — Cut & Glue Sort 20–25 minutes, including the cutting · 4 sheets
12 sets of three side lengths, printed out of order. Students check that the lengths make a triangle, then compare a² + b² with c², and glue each piece in one of three rows: acute, obtuse, or not a triangle. Every piece is close to a right triangle or makes no triangle at all, so remembering 5, 12, 13 does not help.
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Acute, Right, Obtuse, or No Triangle? Classifying by Side Lengths — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each giving three side lengths out of order. Students check that the lengths make a triangle, then compare a² + b² with c² to choose acute, right, obtuse or not a triangle. Every wrong answer is a real mistake: the wrong side taken as c, the comparison turned around, a familiar triple trusted, the triangle check skipped or done with squares, or a drawing that looks right and is not. The row of box numbers at the foot is the check.