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• Pythagorean Theorem
  ...one of the many tools in a good geometer's arsenal. A very large number of geometry problems can be solved by building right triangles and applying the Pythago ...e <math>ABC, CBH, ACH</math> are similar right triangles, and the areas of similar triangles are proportional to the squares of corresponding side lengths,
  5 KB (886 words) - 21:12, 22 January 2024
• MATHCOUNTS
  MATHCOUNTS curriculum includes [[arithmetic]], [[algebra]], [[counting]], [[geometry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MA ...states (most notably Florida), there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representat
  10 KB (1,497 words) - 11:42, 10 March 2024
• Art of Problem Solving
  * [https://artofproblemsolving.com/store/item/intro-geometry Introduction to Geometry] ...n] is an online interactive game for students to participate in activities similar to the [[MATHCOUNTS]] Countdown Round.
  5 KB (667 words) - 17:09, 3 July 2023
• Resources for mathematics competitions
  *[https://www.clevermath.org/ Clevermath] Is similar to above ...olving.com/resources/articles/bary.pdf Barycentric Coordinates in Olympiad Geometry] by Max Schindler and Evan Chen
  24 KB (3,269 words) - 00:43, 24 April 2024
• Math books
  ...eek9], currently a junior in high school. It covers the basics of algebra, geometry, combinatorics, and number theory, along with sets of accompanying practice ...919597 Undergraduate Algebra] by [[Serge Lang]]. Some compare it to being similar to Dummit and Foote with regards to rigor, although this text is slightly m
  24 KB (3,177 words) - 12:53, 20 February 2024
• Menelaus' theorem
  ===Proof with Similar Triangles=== [[Category:Geometry]]
  5 KB (804 words) - 03:01, 12 June 2023
• Fermat's Little Theorem
  A similar version can be used to prove [[Euler's Totient Theorem]], if we let <math>S === Proof 4 (Geometry) ===
  16 KB (2,675 words) - 10:57, 7 March 2024
• Brahmagupta's Formula
  == Similar formulas == A similar formula which Brahmagupta derived for the area of a general quadrilateral i
  3 KB (465 words) - 18:31, 3 July 2023
• Contest strategies
  ..., a visual aid can help solvers visualize and look for clues. Even in non-geometry problems, drawing pictures can help formulate ideas. ...lked about “wishful thinking” — trying to make a problem look like a similar one solved before.
  3 KB (538 words) - 13:13, 16 January 2021
• Incenter/excenter lemma
  In [[geometry]], the '''incenter/excenter lemma''', sometimes called the '''Trillium theo The incenter/excenter lemma makes frequent appearances in olympiad geometry. Along with the larger lemma, two smaller results follow: first, <math>A</m
  2 KB (291 words) - 16:31, 18 May 2021
• Triangle
  ...ctions of the sides summing to 180 degrees. Triangles exist in Euclidean [[geometry]], and are the simplest possible polygon. In [[physics]], triangles are not ...des and is also [[equiangular]]. Note that all equilateral triangles are [[similar]]. All the angles of equilateral triangles are <math>60^{\circ}</math>
  4 KB (628 words) - 17:17, 17 May 2018
• American Scholastic Mathematics Association
  It features questions with probability, counting, arithmetic, algebra, and geometry. It is 35 minutes long and contains 7 questions. The difficulty of this math competition is similar to MOEMS (easier problems) and AMC 8 (harder problems)
  1 KB (153 words) - 13:11, 14 May 2019
• Ptolemy's Inequality
  ...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) - 09:01, 7 June 2023
• 2011 AMC 10B Problems/Problem 22
  [[Category: Introductory Geometry Problems]] Notice that the smaller pyramid on top of the cube is similar to the larger pyramid. Thus, letting <math>x</math> be the edge length of t
  4 KB (691 words) - 18:38, 19 September 2021
• Homothety
  * The resulting image of a polygon from a homothety is [[similar]] to the original polygon. * https://brilliant.org/wiki/euclidean-geometry-homothety/ (contains sample problems and related proofs)
  3 KB (532 words) - 01:11, 11 January 2021
• Power of a Point Theorem
  Draw extra lines to create similar triangles! (Hint: Draw <math>AD</math> on all three figures. Draw another l * [[Geometry]]
  5 KB (827 words) - 17:30, 21 February 2024
• 2006 AIME I Problems/Problem 7
  ...by attaching this triangle with the next trapezoid. Parallel lines give us similar triangles, so we know the proportion of this triangle to the previous trian ...ratio we seed is <math>\frac{33(ay+yx)}{11xy}.</math> Finally note that by similar triangles <math>\frac{x}{x+a} =\frac{y}{y+b} \implies bx = ya.</math> There
  4 KB (709 words) - 01:50, 10 January 2022
• 2006 AMC 12A Problems/Problem 17
  (Similar to Solution 1) [[Category:Introductory Geometry Problems]]
  6 KB (958 words) - 23:29, 28 September 2023
• 2006 AMC 10A Problems/Problem 16
  ...\sim \triangle AEO_2 \sim \triangle AFC</math>. Using the first pair of [[similar triangles]], we write the proportion: [[Category:Introductory Geometry Problems]]
  5 KB (732 words) - 23:19, 19 September 2023
• 2006 AMC 10A Problems/Problem 17
  There are many different similar ways to come to the same conclusion using different [[right triangle|45-45- [[Category:Introductory Geometry Problems]]
  6 KB (1,066 words) - 00:21, 2 February 2023

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