The SSS and SAS similarity criteria
- Same shape, different size — 3 tasks
- Which way round the division goes — 3 tasks
- What the marks give you — 3 tasks
- Where SAS Similarity comes from — 6 tasks
- Going Deeper — 4 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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Similar, or What Is Missing? SSS and SAS Similarity — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pairs of triangles with their side lengths and angles, sorted into three rows: similar by SSS Similarity or SAS Similarity; not proved, because the equal angle is not between the two sides; and not similar, because the sides are not in one ratio. Every side 2 longer, two ratios out of three, and the familiar right triangles all wait in the third row.
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Which Criterion Gets You Out? SSS and SAS Similarity — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a pair of triangles with their numbers or their letters: sides listed out of order, every side 2 longer, two ratios out of three, and an equal angle that is or is not between the two sides. A wrong answer is the mistake the lesson exists to stop, and it goes to a box that sends the student back; the row of box numbers at the foot is the check.
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Do the Facts Prove It? SSS and SAS Similarity — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a set of facts about two triangles: side lengths, ratios like DE/AB = DF/AC, or equal angles. Do the facts prove the triangles similar by SSS Similarity, SAS Similarity or AA? Fill the square if they do, leave it white if not. Sides listed out of order, sides that all grow by the same amount, two ratios out of three, and an equal angle that is not between the two sides all wait among the squares. When every square is right, a letter appears.
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Which Side Goes With Which? SSS and SAS Similarity — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each with two triangles and a pair of equal angles: the two sides at the equal angle in each triangle and the third side of the first are given, and the group finds the third side of the second. The letters are set so that pairing first letter with first letter goes wrong; that mistake lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.