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2. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   AAS (angle-angle-side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°.

3. Isosceles triangle - Wikipedia

   en.wikipedia.org/wiki/Isosceles_triangle

   These include the Calabi triangle (a triangle with three congruent inscribed squares), [10] the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), [11] the 80-80-20 triangle appearing in the Langley's Adventitious Angles puzzle, [12] and the 30-30-120 triangle of the triakis triangular tiling.

4. Pons asinorum - Wikipedia

   en.wikipedia.org/wiki/Pons_asinorum

   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.

5. Congruent isoscelizers point - Wikipedia

   en.wikipedia.org/wiki/Congruent_isoscelizers_point

   An isoscelizer of angle A is a line perpendicular to the bisector of angle A. Let ABC be any triangle. Let P 1 Q 1, P 2 Q 2, P 3 Q 3 be the isoscelizers of the angles A, B, C respectively such that they all have the same length. Then, for a unique configuration, the three isoscelizers P 1 Q 1, P 2 Q 2, P 3 Q 3 are concurrent. The point of ...

6. Solution of triangles - Wikipedia

   en.wikipedia.org/wiki/Solution_of_triangles

   The general spherical triangle is fully determined by three of its six characteristics (3 sides and 3 angles). The lengths of the sides a, b, c of a spherical triangle are their central angles, measured in angular units rather than linear units. (On a unit sphere, the angle (in radians) and length around the sphere are numerically the same. On ...

7. Thales's theorem - Wikipedia

   en.wikipedia.org/wiki/Thales's_theorem

   Since OA = OB = OC, OBA and OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, ∠ OBC = ∠ OCB and ∠ OBA = ∠ OAB. Let α = ∠ BAO and β = ∠ OBC. The three internal angles of the ∆ABC triangle are α, (α + β), and β. Since the sum of the angles of a triangle is equal to 180°, we have

8. Similarity (geometry) - Wikipedia

   en.wikipedia.org/wiki/Similarity_(geometry)

   Any two pairs of angles are congruent, [4] which in Euclidean geometry implies that all three angles are congruent: [a] If ∠BAC is equal in measure to ∠B'A'C', and ∠ABC is equal in measure to ∠A'B'C', then this implies that ∠ACB is equal in measure to ∠A'C'B' and the triangles are similar. All the corresponding sides are ...

9. List of triangle inequalities - Wikipedia

   en.wikipedia.org/wiki/List_of_triangle_inequalities

   The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);