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  2. 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]

  3. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    For example, the sum of the three angles α + β + γ depends on the size of the triangle. In addition, similar triangles cannot be unequal, so the problem of constructing a triangle with specified three angles has a unique solution.

  4. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    An example spangram with corresponding theme words: PEAR, FRUIT, BANANA, APPLE, etc. ... NYT Strands Spangram Answer Today. Today's spangram answer on Saturday, January 18, 2025, is CAPTAIN. ...

  5. Ptolemy's inequality - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_inequality

    For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...

  6. The 13 Best Hinge Prompts That Will Break the Ice in the ...

    www.aol.com/lifestyle/13-best-hinge-prompts...

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  7. Give Your Hinge Matches Something to Respond to With These ...

    www.aol.com/lifestyle/95-hinge-prompt-answers...

    The app allows you to display three Hinge prompt answers, with a myriad of options to choose from (including voice and video prompts!). These range from funny, to deep, to nerdy.

  8. Theon of Smyrna - Wikipedia

    en.wikipedia.org/wiki/Theon_of_Smyrna

    He discusses the Pythagoreans method of looking at harmonies and consonances through half-filling vases and explains these experiments on a deeper level focusing on the fact that the octaves, fifths, and fourths correspond respectively with the fractions 2/1, 3/2, and 4/3. His contributions greatly contributed to the fields of music and physics ...

  9. Hinge joint - Wikipedia

    en.wikipedia.org/wiki/Hinge_joint

    The best examples of ginglymoid joints are the interphalangeal joints of the hand and those of the foot and the joint between the humerus and ulna. The knee joints and ankle joints are less typical, as they allow a slight degree of rotation or of side-to-side movement in certain positions of the limb. The knee is the largest hinge joint in the ...