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  2. Similarity (geometry) - Wikipedia

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

    It can be shown that two triangles having congruent angles (equiangular triangles) are similar, that is, the corresponding sides can be proved to be proportional. This is known as the AAA similarity theorem. [2]

  3. Proportionality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Proportionality_(mathematics)

    The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.

  4. Proportional reasoning - Wikipedia

    en.wikipedia.org/wiki/Proportional_reasoning

    Consider a container of colored liquid inside a right triangle where the triangle can be tilted and the water levels on the left and right side can be measured on a built-in scale. This is called a "water triangle": The water triangle is rotated until it shows a measurement of 4 units on the left side and 6 units on the right side. Suppose the ...

  5. Isosceles triangle - Wikipedia

    en.wikipedia.org/wiki/Isosceles_triangle

    This is an isosceles triangle that is acute, but less so than the equilateral triangle; its height is proportional to 5/8 of its base. [38] The Egyptian isosceles triangle was brought back into use in modern architecture by Dutch architect Hendrik Petrus Berlage. [39] Detailed view of a modified Warren truss with verticals

  6. Intercept theorem - Wikipedia

    en.wikipedia.org/wiki/Intercept_theorem

    The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.

  7. Weber problem - Wikipedia

    en.wikipedia.org/wiki/Weber_problem

    Simpson demonstrated that, in the same way as, in the Fermat triangle problem case, the constructed triangles ABE, ACF, BCG were equilateral because the three attractive forces were equal, in the Weber triangle problem case, the constructed triangles ABE, ACF, BCG, where E, F, G are located outside the ABC triangle, must be proportional to the ...

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  9. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

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