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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. The unchanged properties are called invariants.

  3. Corresponding sides and corresponding angles - Wikipedia

    en.wikipedia.org/wiki/Corresponding_sides_and...

    The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...

  4. 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]

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]

  6. Pons asinorum - Wikipedia

    en.wikipedia.org/wiki/Pons_asinorum

    The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.

  7. Congruence of triangles - Wikipedia

    en.wikipedia.org/wiki/Congruence_of_triangles

    Congruence of triangles may refer to: Congruence (geometry)#Congruence of triangles; Solution of triangles This page was last edited on 28 ...

  8. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.

  9. Yff center of congruence - Wikipedia

    en.wikipedia.org/wiki/Yff_center_of_congruence

    The animation also shows the continuous expansion of the Yff central triangle until the three outer triangles reduce to points on the sides of the triangle. Let ABC be any triangle. Let P 1 Q 1, P 2 Q 2, P 3 Q 3 be the isoscelizers of the angles A, B, C such that the triangle A'B'C' formed by them is the Yff central triangle of ABC.

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