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• 2016 AMC 10A Problems/Problem 24
  ==Solution 9 (Similar Triangles)== ...<math>\overline{CD} = 200</math>, <math>\overline{DF} = 200</math>, and by similar reasoning <math>\overline{AE} = 200</math>.
  24 KB (3,861 words) - 14:17, 26 April 2024
• 2016 AMC 12A Problems/Problem 23
  ==Solution 4: Geometry== == Solution 6: Geometry in 2-D ==
  10 KB (1,700 words) - 16:49, 16 May 2024
• 2016 AMC 10B Problems/Problem 19
  ==Solution 1 (Coordinate Geometry)== ...ath>, we see that <math>\frac{PQ}{EF} = \frac{P'Q'}{E'F}</math> because of similar triangles, and so we only need to find the x-coordinates of <math>P</math>
  11 KB (1,608 words) - 03:18, 23 January 2023
• 2016 AIME II Problems/Problem 14
  ...angle. This means that triangles <math>CQI</math> and <math>CPI</math> are similar. If we let <math>\angle{IDQ}=x</math> and <math>\angle{PDI}=y</math>, then ==Solution 6 (Geometry)==
  15 KB (2,560 words) - 01:44, 1 July 2023
• 2016 AIME II Problems/Problem 10
  ==Solution 2 (Projective Geometry)== ...h>ST</math>, it suffices to find <math>AT\cdot BS</math>. We do this using similar triangles, which can be found by using Power of a Point theorem.
  7 KB (1,090 words) - 22:09, 31 January 2024
• 2016 AMC 8 Problems/Problem 25
  *Note — There are several other following solutions below that use similar methods of finding the area two different ways shown in this solution. Try ==Solution 2: Similar Triangles==
  13 KB (2,115 words) - 16:21, 18 April 2021
• 2016 AMC 8 Problems/Problem 22
  ...abeled E' for convenience. First of all, we can see that EE'H and CE'B are similar triangles because all their three angles are the same. Furthermore, since E ...angle to calculate their area. The two non-colored isosceles triangles are similar, and are in a <math>3:1</math> ratio by AA similarity (alternate interior a
  8 KB (1,157 words) - 16:12, 18 January 2024
• 2017 AMC 10A Problems/Problem 21
  Note that <math>\triangle ABC</math> and <math>\triangle FBE</math> are similar, so <math>\frac{BF}{FE} = \frac{AB}{AC}</math>. This can be written as <mat Similarly, <math>\triangle A'B'C'</math> and <math>\triangle RB'Q</math> are similar, so <math>RB' = \frac{4}{3}y</math>, and <math>C'S = \frac{3}{4}y</math>. T
  3 KB (461 words) - 22:24, 8 January 2023
• 2013 Mock AIME I Problems/Problem 12
  ...ases where <math>t=12-\sqrt{46}</math> and <math>t=12+\sqrt{46}</math> are similar; they merely correspond to two triangles that can each be obtained by refle [[Category:Intermediate Geometry Problems]]
  3 KB (570 words) - 22:37, 8 June 2022
• 2017 AMC 12B Problems/Problem 15
  ...<math>\triangle A'B'C'</math> are both equilateral triangles, they must be similar due to <math>AA</math> similarity. This means that <math>\frac{A'B'}{AB}</m ...to check that <math>B'C' = \sqrt{37}</math>. Since the area ratios of two similar figures is the square of the ratio of their lengths, the ratio is <math>\bo
  9 KB (1,416 words) - 14:30, 23 November 2023
• 2017 AMC 12B Problems/Problem 24
  ...,4a), B=(-1,0), C=(1,0), D=\bigg(1,\frac{1}{a}\bigg)</math>. Then from the similar triangles condition, we compute <math>CE=\frac{4a}{\sqrt{4a^2+1}}</math> an [[Category:Intermediate Geometry Problems]]
  8 KB (1,393 words) - 11:04, 7 October 2023
• 2017 AMC 12B Problems/Problem 9
  A similar solution uses the other intersection point, <math>(-5,8)</math>. [[Category:Introductory Geometry Problems]]
  2 KB (366 words) - 13:54, 15 February 2021
• 2017 AMC 12B Problems/Problem 18
  ==Solution 2: Similar triangles with Pythagorean== ==Solution 3: Similar triangles without Pythagorean==
  7 KB (886 words) - 04:01, 23 January 2023
• 2018 AMC 10A Problems
  ...ways can a student schedule <math>3</math> mathematics courses -- algebra, geometry, and number theory -- in a <math>6</math>-period day if no two mathematics All of the triangles in the diagram below are similar to isosceles triangle <math>ABC</math>, in which <math>AB=AC</math>. Each o
  14 KB (2,171 words) - 21:10, 4 November 2023
• 2017 AIME I Problems/Problem 10
  ==Solution 1 (Coordinates, Geometry)== <math>\angle Z_3Z_1Z_2</math> looks similar to <math>\angle Z_3ZZ_2</math>, so let’s try to prove that they are congr
  13 KB (2,252 words) - 15:46, 6 January 2024
• 2017 AIME I Problems/Problem 15
  ...rge as possible (We will call it <math>T</math>, for convenience) which is similar to <math>S</math> with vertices outside of a unit equilateral triangle <mat ...etween the two triangles. Thus, <math>\triangle XYZ</math> is the triangle similar to <math>S</math> which we were desiring. Our goal now is to maximize the l
  22 KB (3,622 words) - 17:11, 6 January 2024
• 2017 UNCO Math Contest II Problems/Problem 1
  By [[similar triangles]], <math>O_1P</math> is <math>\frac{24}{39}\cdot 52</math> and <m [[Category:Introductory Geometry Problems]]
  1 KB (211 words) - 18:16, 16 January 2023
• 2017 UNCO Math Contest II Problems/Problem 2
  Since the ratio of the areas of two [[similar]] hexagons is the square of the ratio between the side lengths of the hexag [[Category:Introductory Geometry Problems]]
  1 KB (195 words) - 18:22, 16 January 2023
• 1997 JBMO Problems/Problem 1
  We proceed in a similar way to Solution 1. [[Category:Intermediate Geometry Problems]]
  1 KB (233 words) - 11:39, 30 May 2020
• 2008 iTest Problems/Problem 52
  ...e longest side, and let <math>x</math> be the length of the square. Using similar triangles to write a proportion, [[Category:Introductory Geometry Problems]]
  2 KB (252 words) - 13:37, 13 July 2018

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