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- ...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 (885 words) - 22:03, 5 October 2024
- 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 representat10 KB (1,504 words) - 13:10, 1 December 2024
- * [{{SERVER}}/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 (624 words) - 14:58, 13 January 2025
- *[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 Chen17 KB (2,291 words) - 22:33, 13 January 2025
- ...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 m24 KB (3,202 words) - 14:33, 13 January 2025
- ...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, ...into phenomena that were previously difficult to quantify using classical geometry.2 KB (302 words) - 10:17, 27 September 2024
- ===Proof with Similar Triangles=== [[Category:Geometry]]5 KB (804 words) - 02:01, 12 June 2023
- A similar version can be used to prove [[Euler's Totient Theorem]], if we let <math>S === Proof 4 (Geometry) ===16 KB (2,660 words) - 22:42, 28 August 2024
- == Similar formulas == A similar formula which Brahmagupta derived for the area of a general quadrilateral i3 KB (543 words) - 18:35, 29 October 2024
- ..., 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 (544 words) - 13:14, 26 August 2024
- 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</m2 KB (292 words) - 17:22, 14 January 2025
- ...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 (631 words) - 20:16, 8 October 2024
- ...umes the use of a calculator. It encompasses a variety of subjects such as geometry, algebra, and even logic. It features questions with probability, counting, arithmetic, algebra, and geometry. It is 35 minutes long and contains 7 questions.1 KB (164 words) - 22:52, 17 December 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 that3 KB (602 words) - 08:01, 7 June 2023
- [[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 t4 KB (691 words) - 17:38, 19 September 2021
- * 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 (533 words) - 12:51, 2 September 2024
- Draw extra lines to create similar triangles! (Hint: Draw <math>AD</math> on all three figures. Draw another l * [[Geometry]]5 KB (859 words) - 15:11, 8 December 2024
- ...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> There4 KB (709 words) - 00:31, 5 January 2025
- (Similar to Solution 1) [[Category:Introductory Geometry Problems]]6 KB (958 words) - 22:29, 28 September 2023
- ...\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 (811 words) - 10:44, 30 November 2024