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The equality of vertically opposite angles is called the vertical angle theorem. Eudemus of Rhodes attributed the proof to Thales of Miletus. [14] [15] ...
The angle bisector theorem is commonly used when the angle bisectors and side lengths are known. It can be used in a calculation or in a proof. An immediate consequence of the theorem is that the angle bisector of the vertex angle of an isosceles triangle will also bisect the opposite side.
Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle. 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 ...
A transversal produces 8 angles, as shown in the graph at the above left: 4 with each of the two lines, namely α, β, γ and δ and then α 1, β 1, γ 1 and δ 1; and; 4 of which are interior (between the two lines), namely α, β, γ 1 and δ 1 and 4 of which are exterior, namely α 1, β 1, γ and δ.
Proof without words using the inscribed angle theorem that opposite angles of a cyclic quadrilateral are supplementary: 2𝜃 + 2𝜙 = 360° ∴ 𝜃 + 𝜙 = 180° The inscribed angle theorem is used in many proofs of elementary Euclidean geometry of the plane.
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.
Angle bisector theorem (Euclidean geometry) Ankeny–Artin–Chowla theorem (number theory) Anne's theorem ; Apéry's theorem (number theory) Apollonius's theorem (plane geometry) Appell–Humbert theorem (complex manifold) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis)
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 ).