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  1. A triangle is composed of three line segments.[1]
  2. To name a triangle we often use its vertices (the name of the endpoints).[1]
  3. When a triangle has three congruent sides, we call the triangle an equilateral triangle.[1]
  4. When a triangle has two congruent sides it is called an isosceles triangle.[1]
  5. It is usual to name each vertex of a triangle with a single capital (upper-case) letter.[2]
  6. Alternatively, the side of a triangle can be thought of as a line segment joining two vertices.[2]
  7. In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.[3]
  8. If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle.[3]
  9. These angles are formed by two sides of the triangle, which meets at a common point, known as the vertex.[3]
  10. Let us say, ∠1, ∠2 and ∠3 are the interior angles of a triangle.[3]
  11. A vertex is a point where two or more curves, lines, or edges meet; in the case of a triangle, the three vertices are joined by three line segments called edges.[4]
  12. A triangle is usually referred to by its vertices.[4]
  13. Hence, a triangle with vertices a, b, and c is typically denoted as Δabc.[4]
  14. For example, a triangle in which all three sides have equal lengths is called an equilateral triangle while a triangle in which two sides have equal lengths is called isosceles.[4]
  15. At the time, Orlando was still dating Katy Perry, so the blogs were quick to call the whole thing a messy love triangle.[5]
  16. The dim-witted buffoon of commedia dell’arte, pining for his Columbine but outwitted by Harlequin, became the formula for the classic love triangle in opera and theater.[5]
  17. The famous love triangle between Prince Charles, Princess Diana, and Camilla Parker Bowles has been re-created for Season 4 of The Crown.[5]
  18. There was a close up of one of the band members who was playing the triangle.[5]
  19. In this article, we are going to learn about the simplest form of a polygon, a triangle .[6]
  20. As the name suggests, the triangle is a polygon that has three angles.[6]
  21. This is called the angle sum property of a triangle.[6]
  22. In a right-angled triangle, ∆ABC, BC = 26 units and AB = 10 units.[6]
  23. In Geometry, a triangle is the most important shape, defined as a closed two-dimensional diagram containing 3 sides, 3 angles and 3 vertices.[7]
  24. However, sometimes it's hard to find the height of the triangle.[8]
  25. There are a few methods of obtaining right triangle side lengths.[9]
  26. 461 (Volume LIII, Number 11), Quadrant Magazine Limited, page 104: One of the writers' most pleasing inventions was to treat the triangle love story as comedy.[10]
  27. A draughtsman's square in the form of a right-angled triangle.[10]
  28. How Does One Cut a Triangle?[11]
  29. Acute-angled triangle An acute triangle has all its internal angles as acute( i.e.. less than 90°).[12]
  30. Obtuse-angled triangle An obtuse triangle has one of its internal angles as obtuse ( i.e.. greater than 90°).[12]
  31. If all the three sides of a triangle are equal, it is called an equilateral triangle.[12]
  32. In the given triangle, all three sides are equal in length.[12]
  33. If two of its sides are equal, a triangle is called isosceles.[13]
  34. A triangle with all three equal sides is called equilateral.[13]
  35. As regard the angles, a triangle is equiangular if all three of its angles are equal.[13]
  36. Euclid showed that in an isosceles triangle the base angles are equal and, conversely, the sides opposite equal angles are equal.[13]
  37. A triangle with vertices A, B, and C is denoted △ A B C {\displaystyle \triangle ABC} .[14]
  38. In Euclidean geometry , any three points, when non- collinear , determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space ).[14]
  39. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.[14]
  40. An equilateral triangle is also a regular polygon with all angles measuring 60°.[14]
  41. An isosceles triangle can be drawn in many different ways.[15]
  42. A right-angled triangle has one 90° angle.[15]
  43. That 90° angle is shown as a small square where two sides of the triangle join.[15]
  44. It is possible for a triangle to be a right-angled triangle and an isosceles triangle at the same time.[15]
  45. Interestingly, the triangle is the only rigid polygon formed out of straight line segments, meaning that if the three lengths of the sides are given, the measurements correspond to a unique triangle.[16]
  46. Because of this, it is often possible, given some information about a triangle (e.g. some side lengths and some angles), to determine additional facts about the triangle.[16]
  47. The Triangle shape tool offers a handle on the shape and options on the context toolbar to enable the triangle to be modified.[17]
  48. A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon.[18]
  49. Every triangle has three sides and three angles, some of which may be the same.[18]
  50. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and the other two sides being known as the legs.[18]
  51. The study of triangles is sometimes known as triangle geometry, and is a rich area of geometry filled with beautiful results and unexpected connections.[18]

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  • [{'LEMMA': 'triangle'}]
  • [{'LEMMA': '3-gon'}]
  • [{'LEMMA': '2-simplex'}]
  • [{'LEMMA': '∆'}]