Third Triangle Congruence Criterion
Side-Side-Side (SSS)
If three sides of one triangle equal three sides of another, the triangles are congruent.
📋 Review: The First Two Criteria
First Criterion: SAS (Side-Angle-Side)
If two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.
Second Criterion: ASA (Angle-Side-Angle)
If two angles and the included side (the side between those two angles) of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.
🤔 A Natural Question
We've seen that two sides + included angle works (SAS), and two angles + included side works (ASA). But what if we know all three sides are equal? No angles given at all — is this enough to prove congruence?
🔧 Physical Intuition: The Stick Experiment
Imagine you have three sticks (or straws) of fixed lengths — say 5 cm, 7 cm, and 8 cm.
Try to build a triangle with them. Now try to build a different triangle with the same three sticks.
This is because a triangle is a rigid figure. Once the three side lengths are fixed, the shape cannot change.
Contrast with Quadrilaterals
Four rods can form many different shapes — a square can be "squished" into a rhombus. Quadrilaterals are not rigid. But triangles ARE rigid. This is why triangles are used in bridges and buildings!