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In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.
In geometry, the tests for congruence and similarity involve comparing corresponding sides and corresponding angles of polygons. In these tests, each side and each angle in one polygon is paired with a side or angle in the second polygon, taking care to preserve the order of adjacency. [1]
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.
An angle equal to 1 / 2 turn (180° or π radians) is called a straight angle. [5] An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a reflex angle. An angle equal to 1 turn (360° or 2 π radians) is called a full angle, complete angle, round angle or perigon.
The cosine rule gives a and then we are back to Case 1. Case 3: two sides and an opposite angle given (SSA). The sine rule gives C and then we have Case 7. There are either one or two solutions. Case 4: two angles and an included side given (ASA). The four-part cotangent formulae for sets (cBaC) and (BaCb) give c and b, then A follows from the ...
Only one of these angles contains the third side of the triangle in its interior, and this angle is called an interior angle of the triangle. [4] In the picture below, the angles ∠ABC, ∠BCA and ∠CAB are the three interior angles of the triangle. An exterior angle is formed by extending one of the sides of the triangle; the angle between ...
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
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
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