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- ...is defined as the [[set]] (or [[locus]]) of [[point]]s in a [[plane]] with an equal distance from a fixed point. The fixed point is called the [[center] [[Image:circle1.PNG|thumb|right|The radius and center of a circle.]]9 KB (1,585 words) - 12:46, 2 September 2024
- ...nar figure]] consisting of straight [[line segment]]s. There are two types of polygons: [[convex polygon|convex]] and [[concave polygon|concave]]. In their most general form, polygons are an ordered [[set]] of [[vertex|vertices]], <math>\{A_1, A_2, \ldots, A_n\}</math>, <math>n \geq 32 KB (372 words) - 18:04, 30 May 2015
- ...riangles with two sides and an include angle are [[congruent]] by the Side-Angle-Side congruence postulate. ...e <math>A</math>, <math>B</math> and <math>C</math>, respectively, the Law of Cosines states:6 KB (1,003 words) - 23:02, 19 May 2024
- ...ng with figures in a given [[space]]. It is one of the two oldest branches of mathematics, along with [[arithmetic]] (which eventually branched into [[nu ...collegiate]] [[mathematics competitions]] is Euclidean geometry. This type of geometry was first formally outlined by the Greek [[mathematician]] [[Eucli3 KB (478 words) - 00:52, 25 August 2024
- ...he size of the region that a two-[[dimension]]al figure occupies. The size of a region in higher dimensions is referred to as [[volume]]. ...ary means. One can find the area of even more complex regions via the use of [[calculus]].7 KB (1,185 words) - 19:48, 25 November 2024
- ...gle''' is any [[triangle]] with an angle of 90 degrees (that is, a [[right angle]]). ...tenuse is labeled <math>c</math>. The other two sides are called the legs of the triangle.3 KB (499 words) - 22:41, 11 June 2022
- Compute the sum of all the roots of ...stead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?12 KB (1,792 words) - 12:06, 19 February 2020
- ...line{BE}</math>. Point <math>F</math> lies on the circle, on the same side of <math>\overline{BE}</math> as <math>A</math>. Segment <math>AF</math> is ta ...h>B, D</math>, and <math>E</math> are [[collinear]] and contain a diagonal of <math>ABCD</math>. The [[Pythagorean theorem]] results in6 KB (958 words) - 22:29, 28 September 2023
- ...8}</math> if <math>a_1</math>, <math>a_2</math>, <math>a_3\ldots</math> is an arithmetic progression with common difference 1, and <math>a_1+a_2+a_3+\ldo ...is the smallest positive multiple of <math>15</math> such that every digit of <math>n</math> is either <math>8</math> or <math>0</math>. Compute <math>\f6 KB (933 words) - 00:15, 19 June 2022
- ...s of square <math>S_{i+2}.</math> The total area enclosed by at least one of <math>S_{1}, S_{2}, S_{3}, S_{4}, S_{5}</math> can be written in the form < Find the last three digits of the product of the positive roots of6 KB (1,000 words) - 23:25, 26 March 2024
- Find the sum of all positive two-digit integers that are divisible by each of their digits. ...th>27</math> more than the mean of <math>\mathcal{S}</math>. Find the mean of <math>\mathcal{S}</math>.7 KB (1,220 words) - 13:05, 24 November 2024
- ...math> and <math>PR</math> have equal length. Find the square of the length of <math>QP</math>. ...intersects the small circle. This fact can be derived from the application of the Midpoint Theorem to the trapezoid made by dropping perpendiculars from13 KB (2,174 words) - 15:52, 10 November 2024
- ...>A_1</math>, <math>A_n</math>, and <math>B</math> are consecutive vertices of a regular polygon? ...0}{n}</math>, <math>\angle A_nA_1B = \frac{(m-2)180}{m}</math>, and <math>\angle A_2A_1B = 60^{\circ}</math>. Since those three angles add up to <math>360^{3 KB (497 words) - 23:39, 21 December 2018
- ...QB = BC.</math> Angle <math>ACB</math> is <math>r</math> times as large as angle <math>APQ,</math> where <math>r</math> is a positive real number. Find <mat ...h>AP=QB</math>, it also follows that <math>AQ=PC</math>. Now apply the Law of Sines to triangle <math>PBC</math> to find <cmath>\frac{\sin 3x}{BC}=\frac{8 KB (1,275 words) - 02:04, 27 February 2022
- ...> are positive integers, and <math>c</math> is not divisible by the square of any prime. Find <math>a+b+c</math>. ...<math>\angle TCA=75^{\circ}</math>, meaning <math>\triangle TAC</math> is an isosceles triangle and <math>AC=24</math>.4 KB (695 words) - 09:02, 9 October 2024
- ...math> \angle MCA = 23^\circ. </math> Find the number of degrees in <math> \angle CMB. </math> ...triangle ABC</math> such that <math>\angle CBN = 7^\circ</math> and <math>\angle BCN = 23^\circ</math>.7 KB (1,082 words) - 01:08, 30 September 2024
- ...e. Since a triangle has a total of <math>180</math> degrees, each angle of an equilateral triangle has <math>60</math> degrees. ...ral triangle is the simplest [[regular polygon]]. It is also the only type of [[polygon]] that such that the [[equilateral]] polygon must also be the [[e1 KB (186 words) - 18:57, 15 September 2022
- The '''volume''' of an object is a [[measure]] of the [[amount]] of [[space]] that it occupies. Note that volume only applies to three-[[dimens This section covers the methods to find volumes of common [[Euclidean]] objects.3 KB (523 words) - 19:24, 17 August 2023
- ...dicular]] [[line]]s. The [[measure of an angle | measure]] of every right angle is 90 [[degree (geometry) | degrees]] or <math>\frac \pi 2</math> [[radian] * [[Angle]]673 bytes (91 words) - 22:59, 11 June 2022
- ...ex]] of the angle, and the rays themselves are called the [[side]]s of the angle. ...If there is no ambiguity, this notation can be shortened to simply <math>\angle B</math>.4 KB (597 words) - 17:39, 9 May 2024