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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)

    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. In geometry, two figures or objects are congruent if they have the same shape and ...

  4. AA postulate - Wikipedia

    en.wikipedia.org/wiki/AA_postulate

    In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...

  5. Similarity (geometry) - Wikipedia

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

    There are several elementary results concerning similar triangles in Euclidean geometry: [9] Any two equilateral triangles are similar. Two triangles, both similar to a third triangle, are similar to each other (transitivity of similarity of triangles). Corresponding altitudes of similar triangles have the same ratio as the corresponding sides.

  6. Equivalence class - Wikipedia

    en.wikipedia.org/wiki/Equivalence_class

    Congruence is an example of an equivalence relation. The leftmost two triangles are congruent, while the third and fourth triangles are not congruent to any other triangle shown here. Thus, the first two triangles are in the same equivalence class, while the third and fourth triangles are each in their own equivalence class.

  7. Yff center of congruence - Wikipedia

    en.wikipedia.org/wiki/Yff_center_of_congruence

    The four triangles A'P 2 Q 3, Q 1 B'P 3, P 1 Q 2 C', and A'B'C' are always similar. There is a unique set of three isoscelizers P 1 Q 1, P 2 Q 2, P 3 Q 3 such that the four triangles A'P 2 Q 3, Q 1 B'P 3, P 1 Q 2 C', and A'B'C' are congruent. In this special case A'B'C' formed by the three isoscelizers is called the Yff central triangle of ABC. [3]

  8. Similarity system of triangles - Wikipedia

    en.wikipedia.org/wiki/Similarity_System_of_Triangles

    The triangles that make up configurations are known as component triangles. [1] Triangles must not only be a part of a configuration set to be in a similarity system, but must also be directly similar. [1] Direct similarity implies that all angles are equal between two given triangle and that they share the same rotational sense. [2]

  9. 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]

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