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We can use the below rules to judge two triangles are :

1.SSS(Side-Side-Side)(SSS): Triangles with equal sides on three sides are congruent triangles.

2.SAS(Side-Angle-Side)(SAS): A triangle whose sides and their angles correspond to each other is a congruent triangle.

3.ASA(Angle-Side-Angle)(ASA): The two corners and their sides correspond to equal triangles.

4.AAS(Angle-Angle-Side)(AAS): The opposite sides of the two corners and one of the corners correspond to equal triangles.

5.RHS(Right angle-Hypotenuse-Side)(HL): In a pair of right triangles, the hypotenuse is equal to the other right angle. (It proves to use the SSS principle)

But I don't know how to prove these rules to be true.

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  • $\begingroup$ Proved from what? Hilbert takes SAS as an axiom and the rest are proved from it, see e.g. Proof for SSS Congruence. $\endgroup$ – Conifold Jul 1 at 9:46

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