# Proposition: 1.08: "Side-Side-Side" Theorem for the Congruence of Triangles

### (Proposition 8 from Book 1 of Euclid's “Elements”)

If two triangles have two sides equal to two sides, respectively, and also have the base equal to the base, then they will also have equal the angles encompassed by the equal straight lines.

• Let $ABC$ and $DEF$ be two triangles having the two sides $AB$ and $AC$ equal to the two sides $DE$ and $DF$, respectively. (That is) $AB$ to $DE$, and $AC$ to $DF$.
• Let them also have the base $BC$ equal to the base $EF$.
• I say that the angle $BAC$ is also equal to the angle $EDF$.

### Modern Formulation

If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Sections: 24

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014