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In several high school treatments of geometry, the term "exterior angle theorem" has been applied to a different result, [1] namely the portion of Proposition 1.32 which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. This result, which depends upon Euclid's parallel ...
Exterior angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the sum of all three exterior angles, that equals to 360° [9] in the Euclidean case (as for any convex polygon), is less than 360° in the spherical case, and is greater than 360° in the hyperbolic case.
If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264
Desargues' theorem; Droz-Farny line theorem; Encyclopedia of Triangle Centers; Equal incircles theorem; Equal parallelians point; Equidissection; Equilateral triangle; Euler's line; Euler's theorem in geometry; Erdős–Mordell inequality; Exeter point; Exterior angle theorem; Fagnano's problem; Fermat point; Fermat's right triangle theorem ...
Exterior angle theorem (triangle geometry) Extreme value theorem ; F F. and ... Nielsen realization problem (geometric topology) Nielsen–Schreier theorem (free groups)
Quadratrix compass Angle trisection. The trisection of an arbitrary angle using only ruler and compasses is impossible. However, if the quadratrix is allowed as an additional tool, it is possible to divide an arbitrary angle into equal segments and hence a trisection (=) becomes possible.
Propositions twenty-nine to thirty-three deal with an optical problem. He gives a definition of parallels that was generally ridiculed. In propositions one though fifty-seven of On the Section of a Cone, Serenus deals largely with the areas of triangular sections of right and scalene cones that are created by planes passing through the vertex ...
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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