Right triangle congruence: HL
- Naming from the square — 3 tasks
- The same two lengths, two angles — 3 tasks
- Checking HL before you cite it — 3 tasks
- Writing HL into a proof — 3 tasks
- Taking the criterion apart — 9 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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HL, SAS, or Not Settled? Right Triangle Congruence — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pairs of right triangles marked with small squares and ticks, sorted into HL, SAS and not settled. The last row holds the pairs that look like HL and are not: no right angle given, a right angle in one triangle only, or a hypotenuse matched with a leg.
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HL or Not? Right Triangle Congruence — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a pair of marked right triangles or three written lines: HL, SAS, AAS, or not settled? The wrong answers are the two mistakes this lesson exists to stop — using HL without a right angle given or with a hypotenuse matched to a leg, and writing HL for every pair of right triangles. The row of box numbers at the foot is the check.
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Does HL Prove It? Right Triangle Congruence — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a pair of marked triangles or a sentence about two triangles: fill the square if HL proves them congruent, leave it white if it does not. The white squares are the real mistakes: no right angle given, a right angle in one triangle only, a hypotenuse matched with a leg, two legs (that is SAS), a hypotenuse and an angle (AAS). When every square is right, a letter appears.