Create the page "Similar(geometry)" on this wiki! See also the search results found.

• Alcumus
  AoPS generates high-quality solutions for the students to learn and to do similar problems easily. *[[Geometry]]
  3 KB (533 words) - 10:55, 7 February 2023
• 1950 AHSME Problems/Problem 47
  ...gle formed by taking away the rectangle and the two small portions left is similar to the big triangle.Hence, the proportions of the heights is equal to the p [[Category:Introductory Geometry Problems]]
  2 KB (293 words) - 02:24, 11 June 2024
• 2012 AMC 10A Problems/Problem 15
  [[Category: Introductory Geometry Problems]] Triangle <math>EAB</math> is similar to triangle <math>EHI</math>; line <math>HI = 1/2</math>
  6 KB (935 words) - 23:41, 13 September 2023
• 2012 AMC 12A Problems/Problem 16
  ==Solution 9 (Similar Triangles)== [[Category:Introductory Geometry Problems]]
  9 KB (1,496 words) - 02:40, 2 October 2022
• 2012 AMC 12B Problems/Problem 17
  ...In other words, the longer leg is 3 times the shorter leg in any triangle similar to <math>\triangle AGB</math>. ...Triangles <math>\triangle EKM</math> and <math>\triangle MKF</math>, being similar to <math>\triangle AGB</math>, also have legs in a 1:3 ratio, therefore, <m
  12 KB (2,183 words) - 21:05, 23 December 2023
• University of Northern Colorado Math Contest
  ...ey for the Final Round of the contest in late January. The Final Round is similar in spirit to the First Round, but the problems are more challenging. Studen ...e students to exercise their creativity and ingenuity to solve problems in geometry, algebra, combinatorics, probability, and number theory. All the old contes
  2 KB (336 words) - 15:09, 2 January 2020
• 2012 AMC 10B Problems/Problem 23
  We can approach this problem similar to the solution above, by attacking it on the Cartesian plane. As mentioned [[Category: Introductory Geometry Problems]]
  5 KB (851 words) - 11:25, 21 April 2024
• 2012 AIME I Problems/Problem 8
  ...is a right triangular pyramid. Note also that pyramid <math>MPBQ</math> is similar to <math>DPCN</math> with scale factor <math>.5</math> and thus the volume ...nd the volume <math>[DNCMQB]</math> is a sum of areas of cross sections of similar triangles running parallel to face <math>ABFE.</math> Let <math>x</math> be
  10 KB (1,592 words) - 13:35, 4 April 2024
• 1968 IMO Problems/Problem 1
  ...ACB}{2} = \angle ABC</math>, so <math>ABC</math> and <math>ADB</math> are similar by AA Similarity. Hence, <math>c^2 = b(a+b)</math>. Then proceed as in Solu [[Category:Olympiad Geometry Problems]]
  4 KB (729 words) - 08:47, 9 March 2019
• 2012 AIME II Problems/Problem 13
  ...retty much destroyed by complex plane geometry, which is similar to vector geometry only with the power of easy rotation. Place the triangle in the complex pl ...- 2 \alpha</math>. We can use all the congruent equilateral triangles in a similar manner obtaining:
  13 KB (2,052 words) - 18:02, 5 February 2024
• 2012 AIME II Problems/Problem 15
  ...ive up after realizing that angle chasing won't work, you'd likely go in a similar approach to Solution 1 (below) or maybe be a bit more insightful and go wit [[Category:Intermediate Geometry Problems]]
  13 KB (2,298 words) - 12:56, 10 September 2023
• 1988 USAMO Problems/Problem 4
  ...}</math>), so that <math>M</math> is the circumcenter of <math>AIC</math>. Similar results hold for <math>BIC</math> and <math>CIA</math>, and hence <math>O_c [[Category:Olympiad Geometry Problems]]
  3 KB (504 words) - 19:25, 14 October 2021
• 1989 AHSME Problems/Problem 4
  ...m <math>A</math> and <math>B</math>; then the triangle <math>DBY</math> is similar to <math>DEF</math> but with corresponding sides of half the length. [[Category: Introductory Geometry Problems]]
  2 KB (271 words) - 07:42, 22 October 2014
• 1978 USAMO Problems/Problem 2
  .... In this case let AA' and BB' meet at O. Then triangles OAB and OA'B' are similar, so O must represent the same point. So assume A'B' is not parallel to AB. ...oordinate of O equals the y' coordinate of O. Similarly, XOX' and ZOZ' are similar, so OX/OZ = OX'/OZ', so the x-coordinate of O equals its x'-coordinate. In
  4 KB (712 words) - 21:57, 12 November 2023
• 1978 USAMO Problems/Problem 4
  ...gles. Now, since <cmath>WX=2\cdot OW\sin\frac{\angle{WOX}}{2},</cmath> and similar for the other sides, we have that <math>WXYZ</math> is a regular tetrahedro [[Category:Olympiad Geometry Problems]]
  2 KB (322 words) - 23:16, 18 July 2016
• 2013 AMC 12A Problems/Problem 9
  ...al triangles <math>\triangle BDE</math> and <math>\triangle EFC</math> are similar to <math>\triangle ABC</math>, and are therefore also isosceles triangles. [[Category:Introductory Geometry Problems]]
  2 KB (352 words) - 16:25, 12 August 2023
• 2013 AMC 10A Problems/Problem 7
  ...ram of four courses from a menu of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least on Case <math>1</math>: The student chooses both algebra and geometry.
  2 KB (379 words) - 13:06, 1 July 2023
• 2013 AMC 10A Problems/Problem 12
  [[Category: Introductory Geometry Problems]] ...al triangles <math>\triangle BDE</math> and <math>\triangle EFC</math> are similar to <math>\triangle ABC</math>, and are therefore also isosceles triangles.
  2 KB (376 words) - 11:09, 30 July 2022
• 2013 AMC 10B Problems/Problem 15
  ...hexagon can be broken into 6 small equilateral triangles, each of which is similar to the big equilateral triangle. The big triangle's area is 6 times the are [[Category:Introductory Geometry Problems]]
  2 KB (240 words) - 12:18, 18 October 2022
• 2013 AMC 10B Problems/Problem 16
  .../math>. Also, because <math>DE || AC</math>, <math>\triangle ABC</math> is similar to <math>\triangle{DBE}</math> with side length ratio <math>2:1</math>, so [[Category:Introductory Geometry Problems]]
  5 KB (761 words) - 19:33, 11 January 2024

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)