Geometry & measures · Congruence & similarity
Chapter 1 · 4
The idea
Congruent triangles & proof
The four congruence conditions SSS, SAS, ASA/AAS and RHS, why SSA is not one of them, and how to write a congruence proof that earns every mark.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Geometry & measures · Congruence & similarity
Congruent triangles & proof
The four congruence conditions SSS, SAS, ASA/AAS and RHS, why SSA is not one of them, and how to write a congruence proof that earns every mark.
Why it works
Identical — same shape, same size
Congruent means identical — same shape, same size. One shape can be picked up, turned, flipped and laid exactly on the other. Reflections, rotations and translations all produce congruent images; enlargements (except by factor ) do not — they change the size, and congruence is precisely "the size survived".Three right facts pin it down
A triangle has three sides and three angles, but the right three facts pin it down completely. There are exactly four such sets:| Condition | What you need |
|---|---|
| SSS | all three pairs of sides equal |
| SAS | two sides and the angle between them |
| ASA / AAS | two angles and a corresponding side |
| RHS | right angle, hypotenuse and one other side |
Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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