Relevant bibliographies by topics / Angle bisector theorem

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Angle bisector theorem'

Author: Grafiati
Published: 24 April 2022

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Journal articles on the topic "Angle bisector theorem"

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Conway, John, and Alex Ryba. "The Steiner-Lehmus angle-bisector theorem." Mathematical Gazette 98, no. 542 (2014): 193–203. http://dx.doi.org/10.1017/s0025557200001236.

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In 1840 C. L. Lehmus sent the following problem to Charles Sturm: ‘If two angle bisectors of a triangle have equal length, is the triangle necessarily isosceles?’ The answer is ‘yes’, and indeed we have thereverse-comparison theorem: Of two unequal angles, the larger has the shorter bisector (see [1, 2]).Sturm passed the problem on to other mathematicians, in particular to the great Swiss geometer Jakob Steiner, who provided a proof. In this paper we give several proofs and discuss the old query: ‘Is there a direct proof?’ before suggesting that this is no longer the right question to ask.We g
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Byrkit, Donald R., and Timothy L. Dixon. "Some Theorems Involving the Lengths of Segments in a Triangle." Mathematics Teacher 80, no. 7 (1987): 576–79. http://dx.doi.org/10.5951/mt.80.7.0576.

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Many theorems in geometry concern the relationships among the lengths of various line segments of a triangle. One theorem of elementary geometry states that the segments into which an angle bisector divides the opposite sides of a triangle are in proportion to the adjacent sides.
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Lu, Jitan, and Raymond Scacalossi. "Delving Deeper: A Tale Of Two Theorems." Mathematics Teacher 98, no. 5 (2005): 338–43. http://dx.doi.org/10.5951/mt.98.5.0338.

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This month's offering consists of two articles. Jitan Lu shows that a triangle is determined by its three angle bisectors. Then Raymond Scacalossi describes an incident in his Advanced Placement calculus class where a student–invented method that seemed implausible turned out to be valid.
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ia, Amel, Mas hadi, and Sri Gemawati. "Alternative Proofs for the Length of Angle Bisectors Theorem on Triangle." International Journal of Mathematics Trends and Technology 66, no. 10 (2020): 163–66. http://dx.doi.org/10.14445/22315373/ijmtt-v66i10p519.

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Hajja, Mowaffaq. "The arbitrariness of the semi-angle-bisectors of a triangle." Mathematical Gazette 106, no. 565 (2022): 78–83. http://dx.doi.org/10.1017/mag.2022.12.

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Figure 1 shows a triangle ABC with the midpoints A′, B′ and C′ of its sides. The line segments AA′, BB′ and CC′ are called the medians, and the point G of their intersection the centroid. The line segments AG, BG and CG will be called, for lack of a better name, the semi-medians. It is interesting that the medians of any triangle can serve as the side lengths of some triangle. This property of the medians is referred to as the median triangle theorem in [1, §473, page 282], and is discussed, together with generalisations to tetrahedra and higher dimensional simplices, in [2].
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Abu-Saymeh, Sadi, and Mowaffaq Hajja. "More variations on the Steiner-Lehmus theme." Mathematical Gazette 103, no. 556 (2019): 1–11. http://dx.doi.org/10.1017/mag.2019.1.

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The celebrated Steiner-Lehmus theorem states that if the internal bisectors of two angles of a triangle are equal, then the triangle is isosceles. In other words, if P is the incentre of triangle ABC, and if BP and CP meet the sides AC and AB at B′and C′, respectively, then
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Josefsson, Martin. "Further characterisations of tangential quadrilaterals." Mathematical Gazette 101, no. 552 (2017): 401–11. http://dx.doi.org/10.1017/mag.2017.122.

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Tangential quadrilaterals are defined to be quadrilaterals in which a circle can be inscribed that is tangent to all four sides. It is well known and easy to prove that a convex quadrilateral is tangential if, and only if, the angle bisectors of all four vertex angles are concurrent at a point, which is the centre of the inscribed circle (incircle). The most well-known and in problem solving useful characterisation of tangential quadrilaterals is Pitot's theorem, which states that a convex quadrilateral is tangential if and only if its consecutive sides a, b, c, d satisfy the relation a + c =
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Surlina, Surlina, Mashadi Mashadi, and Sri Gemawati. "PENGEMBANGAN TEOREMA SAWAYAMA-THEBAULT MENGGUNAKAN EXCENTER." JURNAL MATHEMATIC PAEDAGOGIC 3, no. 1 (2018): 19. http://dx.doi.org/10.36294/jmp.v3i1.270.

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AbstractA triangle have special lines, such as angle bisectors and perpendicular bisector.These special lines are concurrent with their corresponding concurrent points, and called incenter, excenter and circumcenter. This paper discusses how to prove the collinear point of Sawayama-Thebault’s circle using excenter. Then, it is proved the three points collinear using simple ways, like similarity triangles and Thales theorem.Keywords: Sawayama-Thebault’s theorem, excenter, collinearAbstrakSegitiga memiliki beberapa garis-garis istimewa, diantaranya garis bagi, dan garis sumbu. Garis-garis istime
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Charles, D. D., H. H. Rieke, and R. Purushothaman. "Well-Test Characterization of Wedge-Shaped, Faulted Reservoirs." SPE Reservoir Evaluation & Engineering 4, no. 03 (2001): 221–30. http://dx.doi.org/10.2118/72098-pa.

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Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smoot
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O'ROURKE, JOSEPH. "COMPUTATIONAL GEOMETRY COLUMN 23." International Journal of Computational Geometry & Applications 04, no. 02 (1994): 239–42. http://dx.doi.org/10.1142/s0218195994000148.

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Three open problems on tetrahedralizations are described: Does bisection refinement keep solid angles bound away from zero? Can a tetrahedralization be frozen with respect to flips? Do points in convex position have a Hamiltonian tetrahdralization?
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Dissertations / Theses on the topic "Angle bisector theorem"

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Gardner, Sherri R. "A Variety of Proofs of the Steiner-Lehmus Theorem." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etd/1169.

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The Steiner-Lehmus Theorem has garnered much attention since its conception in the 1840s. A variety of proofs resulting from the posing of the theorem are still appearing today, well over 100 years later. There are some amazing similarities among these proofs, as different as they seem to be. These characteristics allow for some interesting groupings and observations.
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Book chapters on the topic "Angle bisector theorem"

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"The Steiner- Lehmus Angle- Bisector Theorem." In The Best Writing on Mathematics 2015. Princeton University Press, 2016. http://dx.doi.org/10.1515/9781400873371-016.

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Conway, John, and Alex Ryba. "The Steiner-Lehmus Angle-Bisector Theorem." In The Best Writing on Mathematics 2015. Princeton University Press, 2016. http://dx.doi.org/10.2307/j.ctvc778jw.18.

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