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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 ABC with its right angle at C, hypotenuse c, and legs a and b,. 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).

  4. Garfield's proof of the Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Garfield's_proof_of_the...

    Diagram to explain Garfield's proof of the Pythagorean theorem. In the figure, is a right-angled triangle with right angle at . The side-lengths of the triangle are ,,. Pythagorean theorem asserts that = +.

  5. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    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 angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. [1]

  6. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    The triangle angle sum theorem states that the sum of the three angles of any triangle, in this case angles α, β, and γ, will always equal 180 degrees. The Pythagorean theorem states that the sum of the areas of the two squares on the legs ( a and b ) of a right triangle equals the area of the square on the hypotenuse ( c ).

  7. Sum of angles of a triangle - Wikipedia

    en.wikipedia.org/wiki/Sum_of_angles_of_a_triangle

    Triangle area property: The area of a triangle can be as large as we please. Three points property: Three points either lie on a line or lie on a circle. Pythagoras' theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. [1]

  8. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then ⁡ =, and the law of cosines reduces to = +. The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.

  9. Special right triangle - Wikipedia

    en.wikipedia.org/wiki/Special_right_triangle

    Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, ⁠ π / 2 ⁠ radians) and two other congruent angles each measuring half of a right angle (45°, or ...

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