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  2. 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.

  3. Right triangle - Wikipedia

    en.wikipedia.org/wiki/Right_triangle

    A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1⁄4 turn or 90 degrees). The side opposite to the right angle is called the hypotenuse (side in the figure). The sides adjacent to the right angle are called ...

  4. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    Thales's theorem. Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle. In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed ...

  5. Special right triangle - Wikipedia

    en.wikipedia.org/wiki/Special_right_triangle

    The Kepler triangle is a right triangle whose sides are in geometric progression. If the sides are formed from the geometric progression a, ar, ar 2 then its common ratio r is given by r = √ φ where φ is the golden ratio. Its sides are therefore in the ratio 1 : √ φ : φ. Thus, the shape of the Kepler triangle is uniquely determined (up ...

  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. It is equivalent to the theorem about ratios in ...

  7. Kepler triangle - Wikipedia

    en.wikipedia.org/wiki/Kepler_triangle

    A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is where is the golden ratio, and the progression can be written: , or approximately . Squares on the edges of this triangle have areas in another geometric progression, . Alternative definitions of the same triangle ...

  8. Proportionality (mathematics) - Wikipedia

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

    In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant).

  9. Geometric mean theorem - Wikipedia

    en.wikipedia.org/wiki/Geometric_mean_theorem

    In Euclidean geometry, the geometric mean theorem or right triangle altitude theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude. Expressed as a mathematical formula, if h denotes the ...