Congruent shapes and congruent triangles
Slide, turn and flip a shape onto another. Then match the corresponding vertices of two triangles, choose the congruence condition, write a proof line by line, and drag a counterexample that shows SSA is not a condition.
- UK: Year 9
- France: grade 8
- Germany: grade 7
- Iran: grade 7
- Afghanistan: grade 7
- Syria: grade 8
- Palestine: grade 8
- Ukraine: grade 5
- Russia: grade 5
Guide
This studio is for Years 8–9 (KS3 "criteria for congruence of triangles": SSS, SAS, ASA, RHS).
Two shapes are congruent if one can be slid, turned or flipped to fit exactly on the other. Then corresponding sides and angles are equal. The order of the letters in "triangle ABC is congruent to triangle DEF" matters: A goes onto D, B onto E and C onto F.
You don't need to check all six parts. These conditions are enough: three sides (SSS), two sides and the angle between them (SAS), two angles and the side between them (ASA), and for right-angled triangles the hypotenuse and one side (RHS). Three angles (AAA), or two sides and an angle that is not between them (SSA), are not enough.
In a proof every line has a statement and a reason: given, common side, vertically opposite angles, a congruence condition, or corresponding parts of congruent triangles. "It looks equal in the picture" is not a reason.