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• 2014 AMC 10A Problems/Problem 12
  [[Category: Introductory Geometry Problems]] This solution is very similar to the one above, but instead we use the solutions to guide us. The interio
  3 KB (482 words) - 11:50, 7 September 2021
• 2014 AMC 10A Problems/Problem 16
  [[Category: Introductory Geometry Problems]] ...eight of <math>AFB</math>. Since <math>XHY</math> and <math>DHC</math> are similar for the same reasons as <math>XFY</math> and <math>AFB</math>, the height o
  9 KB (1,411 words) - 19:51, 25 July 2023
• 2014 AMC 10A Problems/Problem 19
  [[Category: Introductory Geometry Problems]] ...t is inside the cube with side length <math>3</math> be <math>x</math>. By similar triangles, <math>\dfrac{x}{3}=\dfrac{2\sqrt{33}}{10}</math>, giving <math>x
  3 KB (377 words) - 21:23, 28 October 2023
• 2014 AMC 10A Problems/Problem 22
  [[Category: Introductory Geometry Problems]] ==Solution 6 (Pure Euclidian Geometry)==
  13 KB (1,983 words) - 12:39, 7 June 2024
• 1963 AHSME Problems/Problem 18
  ...y selection of <math>U</math>, as described, <math>\triangle EUM</math> is similar to: ...A</math>. This leads to prediction that <math>\triangle FEA</math> is the similar triangle as it shares an angle, and to prove this, we need to show that <ma
  2 KB (410 words) - 21:18, 31 May 2020
• 1994 USAMO Problems/Problem 3
  ...he triangles <math>\triangle AEC</math> and <math>\triangle QED</math> are similar. Therefore, <math>\triangle AEC</math> and <math>\triangle QED</math> are similar, so <math>AC/CE=QD/DE</math>.
  4 KB (747 words) - 08:02, 19 July 2016
• 2014 AMC 12A Problems/Problem 20
  [[Category: Introductory Geometry Problems]] This problem is similar to [https://en.wikipedia.org/wiki/Fagnano%27s_problem Fagnano's Problem].
  4 KB (665 words) - 04:35, 22 January 2024
• 2014 AMC 10B Problems/Problem 23
  [[Category: Introductory Geometry Problems]] ...<math>r_1</math> and height <math>h</math>. The smaller right triangle is similar to the blue highlighted one in Solution <math>1</math>. Then <math>\frac{r_
  6 KB (1,060 words) - 19:15, 11 August 2023
• 2014 AMC 12B Problems/Problem 21
  ...nt of <math>AB</math>. So <math>\triangle AJG</math>, along with all other similar triangles in the picture, is a 30-60-90 triangle, and we have <math>AG=\sqr ...>\triangle KEJ, \triangle JAG, \triangle GDH, \triangle HFK</math> are all similar. Using proportions and the pythagorean theorem, we find
  8 KB (1,307 words) - 02:07, 1 January 2023
• 1964 AHSME Problems/Problem 35
  A similar computation using <math>\triangle AEB</math> and <math>\triangle CEB</math> [[Category:Introductory Geometry Problems]]
  6 KB (892 words) - 00:02, 12 July 2023
• 1964 AHSME Problems/Problem 29
  ...rtional, and the included angles are congruent, then the two triangles are similar by SAS congruence. Therefore, the third pair of sides must also be in the [[Category:Introductory Geometry Problems]]
  2 KB (331 words) - 22:59, 29 June 2023
• 1993 AHSME Problems/Problem 27
  ...th> as the circle moves around the triangle. It turns out this triangle is similar to the <math>6-8-10</math> triangle (Proof: Realize that the slope of the l [[Category: Intermediate Geometry Problems]]
  3 KB (420 words) - 11:10, 18 July 2020
• 1992 AHSME Problems/Problem 11
  ...ircle intersects <math>BC</math> as <math>E</math>. So <math>ABC</math> is similar to <math>DEC</math>. Since <math>DE</math> is the radius of the smaller cir [[Category:Introductory Geometry Problems]]
  2 KB (324 words) - 12:02, 24 November 2016
• 1991 AHSME Problems/Problem 22
  ...the radius of the smaller circle be <math>y</math>, we can see that, using similar triangle, <math>x=2y</math>. In addition, the total hypotenuse of the large [[Category: Intermediate Geometry Problems]]
  2 KB (295 words) - 19:09, 11 October 2016
• 1990 AHSME Problems/Problem 4
  <math>DFE</math> and <math>AFB</math> are similar triangles, so <math>FD</math> is one quarter the length of the correspondin [[Category: Introductory Geometry Problems]]
  1 KB (180 words) - 20:41, 2 July 2021
• 1990 AHSME Problems/Problem 28
  ...ic, we see that quadrilaterals <math>AXOW</math> and <math>OYCZ</math> are similar. [[Category: Intermediate Geometry Problems]]
  2 KB (335 words) - 11:51, 5 October 2019
• 1952 AHSME Problems/Problem 49
  == Alternative but very similar Solution == ...\frac{1}{3}K+\frac{1}{3}K+\frac{1}{3}K = K.</math> Then we can implement a similar but different area addition postulate to the first solution. It will be <ma
  7 KB (1,136 words) - 10:01, 23 December 2023
• 2015 AMC 10B Problems/Problem 22
  ...de length. I chose to write it in terms of <math>FG</math> so we can apply similar triangles easily. To simplify the process lets write <math>FG</math> as <ma [[Category: Introductory Geometry Problems]]
  7 KB (1,146 words) - 14:09, 13 April 2024
• 2007 iTest Problems/Problem 42
  ...line as seen in the diagram is <math>100\sqrt{2} - 100</math> feet. Using similar triangles, the height of the smaller triangle is <math>50\sqrt{2} - 50</mat [[Category:Intermediate Geometry Problems]]
  3 KB (524 words) - 23:01, 17 June 2018
• 2007 IMO Problems/Problem 4
  ...s presents us <math>\dfrac{PK}{QL}=\dfrac{PK}{QD}=\dfrac{PC}{QC}</math> by similar triangles; now, we have only to prove <math>\dfrac{PC}{QC}=\dfrac{RQ}{RP}</ ...rea of <math>RPK.</math> Finding the area of <math>\triangle RQL</math> is similar.
  8 KB (1,480 words) - 14:52, 5 August 2022

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