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  2. Congruence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Congruence_(geometry)

    The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles.

  3. Hinge theorem - Wikipedia

    en.wikipedia.org/wiki/Hinge_theorem

    In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. [1]

  4. Congruence of triangles - Wikipedia

    en.wikipedia.org/wiki/Congruence_of_triangles

    Download as PDF; Printable version; In other projects ... move to sidebar hide. Congruence of triangles may refer to: Congruence (geometry)#Congruence of triangles ...

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    Two triangles that are congruent have exactly the same size and shape. All pairs of congruent triangles are also similar, but not all pairs of similar triangles are congruent. Given two congruent triangles, all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length.

  6. Saccheri–Legendre theorem - Wikipedia

    en.wikipedia.org/wiki/Saccheri–Legendre_theorem

    Similarly, the existence of at least one triangle with angle sum of less than 180 degrees implies the characteristic postulate of hyperbolic geometry. [ 3 ] One proof of the Saccheri–Legendre theorem uses the Archimedean axiom , in the form that repeatedly halving one of two given angles will eventually produce an angle sharper than the ...

  7. Hilbert's axioms - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_axioms

    Congruence [ edit ] If A , B are two points on a line a , and if A ′ is a point upon the same or another line a ′, then, upon a given side of A ′ on the straight line a ′, we can always find a point B ′ so that the segment AB is congruent to the segment A ′ B ′.

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