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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]
The hinge theorem or 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.
The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle. In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.
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For example, in the book Topology and Groupoids, where the condition given for the statement below is that and . The pasting lemma is crucial to the construction of the fundamental group and fundamental groupoid of a topological space ; it allows one to concatenate paths to create a new path.
A top Federal Reserve official said Monday that he is leaning toward supporting an interest rate cut when the Fed meets in two weeks but that evidence of persistent inflation before then could ...
How Cialis Works. Cialis is a prescription medication designed to treat ED. It’s approved for this use by the U.S. Food and Drug Administration (FDA). Tadalafil is the active ingredient in Cialis.
More generally, the constructibility of all powers of 5 greater than 5 itself by marked ruler and compass is an open problem, along with all primes greater than 11 of the form p = 2 r 3 s 5 t + 1 where t > 0 (all prime numbers that are greater than 11 and equal to one more than a regular number that is divisible by 10).