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  • The '''Pythagorean Theorem''' states that for a [[right triangle]] with legs of length <math>a</math> and <math>b</math> and [[hypotenuse]] In these proofs, we will let <math>ABC </math> be any right triangle with a right angle at <math>\angle ACB</math>.
    5 KB (885 words) - 22:03, 5 October 2024
  • ...st intersects the side of length 5; By letting the bottom left side of the triangle be defined as (0,0), its slope is <math>m = \frac{1-4}{8-0} = -\frac{3}{8}< The second line's equation can be found in a similar fashion. Its slope is <math>m = \frac{0-5}{7-1} = -\frac{5}{6}</math>
    8 KB (1,016 words) - 23:17, 30 December 2023
  • ...ns that no matter how much you zoom in on a fractal, its structure remains similar at every scale. This concept of self-similarity is a hallmark of fractals, ...xample of a fractal, this curve is constructed by repeatedly subdividing a triangle, resulting in a shape with infinite perimeter but finite area.
    2 KB (302 words) - 10:17, 27 September 2024
  • *Let <math>ABC</math> be a triangle such that ...us]], respectively. Prove that triangle <math>ABC </math> is similar to a triangle <math>T </math> whose side lengths are all positive integers with no common
    13 KB (2,048 words) - 14:28, 22 February 2024
  • ...ty]] of points on each of the three sides (extended when necessary) of a [[triangle]]. If line <math>PQ</math> intersecting <math>AB</math> on <math>\triangle ABC</math>, where <math>P</math> is on <math>BC</math>, <math>Q</math> is o
    5 KB (804 words) - 02:01, 12 June 2023
  • ...h>, let <math>L</math> be the midpoint of <math>\overarc{BC}</math> on the triangle's circumcenter. Then, the theorem states that <math>L</math> is the center ...or). We are going to show that <math>LB = LI</math>, the other cases being similar.
    2 KB (291 words) - 15:31, 18 May 2021
  • A '''triangle''' is a type of [[polygon]]. {{asy image|<asy>draw((0,1)--(2,0)--(3,2)--cycle);</asy>|right|A triangle.}}
    4 KB (631 words) - 20:16, 8 October 2024
  • ...the case where <math>F</math> is concave. The proof for the other case is similar. * Prove that for any <math>\triangle ABC</math>, we have <math>\sin{A}+\sin{B}+\sin{C}\leq \frac{3\sqrt{3}}{2}</
    3 KB (628 words) - 05:29, 28 November 2024
  • ...math>P </math> such that the [[triangles]] <math>APB, \; DCB </math> are [[similar]] and have the same [[orientation]]. In particular, this means that ...rity]], we also know that the triangles <math>ABD, \; PBC </math> are also similar, which implies that
    3 KB (602 words) - 08:01, 7 June 2023
  • ...gle is the diagonal of the pyramid's base. This is a <math>45-45-90</math> triangle. Also, we can let the dimensions of the rectangle be <math>s</math> and <ma ...to the base, and they share a <math>45^\circ</math> angle with the larger triangle. Therefore, the legs of the right triangles can be expressed as <math>s.</m
    4 KB (691 words) - 17:38, 19 September 2021
  • * The resulting image of a polygon from a homothety is [[similar]] to the original polygon. ...ath> <math>\omega_{B},</math> and <math>\omega_{C}</math>. If the sides of triangle <math>ABC</math> are <math>13,</math> <math>14,</math> and <math>15,</math>
    3 KB (533 words) - 12:51, 2 September 2024
  • ...math> passes through the vertices <math>A</math> and <math>C</math> of the triangle <math>ABC</math> and intersects the segments <math>AB</math> and <math>BC</ Consider <math>\triangle MKA </math> and <math>\triangle MNC</math>, they are similar because <math>\angle MAK</math> = <math>\angle MCN</math>, and also <math>\
    3 KB (496 words) - 12:35, 18 January 2023
  • Draw extra lines to create similar triangles! (Hint: Draw <math>AD</math> on all three figures. Draw another l ...rc <math>AB</math>). If <math>AP = 20</math>, find the perimeter of <math>\triangle PQR</math>.
    5 KB (859 words) - 15:11, 8 December 2024
  • Since the area of the triangle is equal to <math>\frac{1}{2}bh</math>, ...r of trapezoids. Let one side length (not on a parallel line) of the small triangle be <math>x</math> and the area of it be <math>x^2</math>. Also, let all sec
    4 KB (709 words) - 00:50, 10 January 2022
  • ...th of the third side is 15. What is the greatest possible perimeter of the triangle? Rhombus <math>ABCD</math> is similar to rhombus <math>BFDE</math>. The area of rhombus <math>ABCD</math> is 24,
    13 KB (2,058 words) - 11:36, 4 July 2023
  • Rhombus <math> ABCD</math> is similar to rhombus <math> BFDE</math>. The area of rhombus <math> ABCD</math> is 2 .... Since <math>\angle BAD=60 </math>, <math>\triangle ADB</math> and <math>\triangle DBC</math> are equilateral. <math>DB</math>, which is equal to <math>AB</ma
    3 KB (447 words) - 02:49, 16 January 2021
  • ...}</math> is tangent to the circle. Using the Pythagorean Theorem on <math>\triangle AFE</math>, then, we see ...>, <math>\angle ADE = 135^\circ</math>. Using the Law of Cosines on <math>\triangle ADE</math>, we see
    6 KB (958 words) - 22:29, 28 September 2023
  • ...and <math>\overline{AC}</math> are congruent. What is the area of <math>\triangle ABC</math>? How many non-similar triangles have angles whose degree measures are distinct positive integers
    13 KB (2,028 words) - 15:32, 22 March 2022
  • ...and <math>\overline{AC}</math> are congruent. What is the area of <math>\triangle ABC</math>? Let their tangent points to <math>\triangle ABC</math> be <math>D</math> and <math>E</math>, respectively.
    5 KB (811 words) - 10:44, 30 November 2024
  • ...\frac 12AH = 1</math>, so <math>\triangle BWZ</math> is a <math>45-45-90 \triangle</math>. Hence <math>WZ = \frac{1}{\sqrt{2}}</math>, and <math>[WXYZ] = \lef ...ferent similar ways to come to the same conclusion using different [[right triangle|45-45-90 triangles]].
    6 KB (1,106 words) - 09:20, 4 November 2024

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