Side-side-side congruence

Builds on Congruent triangles Euclidean distance

Statement

Let $ABC$ and $A'B'C'$ be triangles in the Euclidean space $\mathbb{R}^n$ , and let $d$ be the Euclidean distance. Then $ABC$ and $A'B'C'$ are congruent if and only if $d(A, B) = d(A', B'), \quad d(B, C) = d(B', C') \quad \text{and} \quad d(C, A) = d(C', A').$

Remarks

Other criteria for congruence are side-angle-side, angle-side-angle and angle-angle-side. Side-side-angle is not a criterion: two sides and an angle that is not between them can fit two different triangles. Angle-angle-angle is not a criterion either. Triangles with equal angles are similar, but they can have different sizes.

Reading path

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Tag	`0BRBYRK6PA`
URI	`m2://0BRBYRK6PA`
Aliases	`sss-congruence`
Kind	statement, theorem
Writing	W0 stub
MSC	51M04
Status	This copy of the site has no build data. Run `m2 status 0BRBYRK6PA`.
Uses	Congruent triangles, Euclidean distance

Side-side-side congruence

Statement

Remarks

Reading path

Further reading

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What links here