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  2. 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 ...

  3. Congruence (geometry) - Wikipedia

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

    This diagram illustrates the geometric principle of angle-angle-side triangle congruence: given triangle ABC and triangle A'B'C', triangle ABC is congruent with triangle A'B'C' if and only if: angle CAB is congruent with angle C'A'B', and angle ABC is congruent with angle A'B'C', and BC is congruent with B'C'.

  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. Congruence of triangles - Wikipedia

    en.wikipedia.org/wiki/Congruence_of_triangles

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  6. Similarity (geometry) - Wikipedia

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

    Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.

  7. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter.