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- ...denoted by <math>\measuredangle</math> instead of the conventional <math>\angle</math>. We know that <cmath>\measuredangle ADB = 90^{\circ} = \measuredangl ...</math> bisects <math>\angle EDF</math> and <math>HE</math> bisects <math>\angle FED</math>.8 KB (1,408 words) - 08:39, 10 July 2024
- ...rection and magnitude." For Euclidean geometers, a vector is essentially a directed line segment. In many situations, a vector is best considered as an n-tuple ...this coordinate form as an ordered <math>n</math>-tuple of numbers within angle brackets or parentheses, <math>(x\,\,y\,\,z\,\,...)</math>. The set of vect11 KB (1,876 words) - 18:01, 29 August 2024
- If <math>\theta</math> is the [[directed angle]] between the <math>x</math>-axis and <math>\mathcal L</math>, the slope is1 KB (192 words) - 20:02, 29 September 2006
- We will use directed angles mod <math> \displaystyle \pi </math>. ...ngle B_1PQ = \angle B_2PQ </math>. This means that <math> \angle CA_1Q = \angle CA_2Q </math>, so <math> \displaystyle C, A_1, A_2, Q </math> are concyclic3 KB (470 words) - 06:32, 28 March 2007
- We use directed angles mod <math> \displaystyle \pi </math>. ...ystyle DFC, DAF </math> are similar. Since these triangles share a common angle, it then suffices to show <math> \frac{DC}{DF} = \frac{DF}{DA} </math>, or10 KB (1,539 words) - 22:37, 6 June 2007
- ...jective sense. Thus we will prove the theorem for a cyclic hexagon, using directed angles mod <math>\pi </math>. ...le MNB \equiv \angle MND \equiv 180^\circ - \angle MCD \equiv 180^\circ - \angle ACD </math>.5 KB (833 words) - 14:23, 6 July 2024
- ...existence of cyclic quadrilaterals in a geometry problem often suggests [[angle chasing]]. Given a nondegenerate, [[convex]] quadrilateral <math>ABCD</math * <math>\angle ACB</math> and <math>\angle ADB</math> are equal (this also holds for three other pairs of angles, foun2 KB (291 words) - 04:30, 16 August 2011
- ...that <math>B_1'=B_1</math> and <math>Q' =Q</math>. All our angles will be directed, and measured mod <math>\pi</math>. <cmath> \angle C_1 Q' P \equiv \angle C_1 B_1' P \equiv \angle A B_1' P . </cmath>6 KB (1,117 words) - 00:17, 11 October 2021
- We use directed angles mod <math>\pi</math>. Since <math>\angle ADB</math> and <math>\angle AEB</math> are both right angles, points <math>ABDE</math> are concyclic.2 KB (345 words) - 17:42, 13 April 2008
- We will use directed angles mod <math>\pi</math>, and directed arcs mod <math>2\pi</math>. ...equiv \tfrac{1}{2} (\widehat{MN} + \widehat{AS}) \equiv \angle MIS \equiv \angle I_a IS . </cmath>3 KB (437 words) - 14:47, 27 April 2008
- ...</math> is cyclic if and only if <math>\overline{BG}</math> bisects <math>\angle CBD</math>. We will use directed angles in this solution. Extend <math>QR</math> to <math>T</math> as follow6 KB (973 words) - 18:24, 18 October 2018
- lines <math>AX, BX, AZ, BZ</math>, respectively. Prove that the acute angle ...ed by lines <math>PQ</math> and <math>RS</math> is half the size of <math>\angle XOZ</math>, where13 KB (2,274 words) - 02:15, 22 September 2024
- so the (directed) distance from any point <math>(x,y,z)</math> to the plane is <math>ax+by+c ...contains <math>C</math> and the <math>\text{centroid}</math>. We seek the angle <math>\theta</math> of the line:<math>(1)</math> through the centroid <math4 KB (633 words) - 12:20, 31 August 2024
- ..., and <math>\angle A'HX=\angle FIX=m(FX)/2</math>. So <math>\angle C'HJ = \angle A'HX</math>. Since <math>J</math>, <math>H</math>, and <math>X</math> are c ...hen <math>2\theta=\angle FBH=\angle C'HB</math>, and so <math>\angle C'HB=\angle AHB</math>. It follows that <math>P_1'</math> is on <math>\overleftrightarr15 KB (2,593 words) - 12:37, 29 January 2021
- where directed lengths are used on the right side. ...&= \frac{\sin(\angle{AOC})\sin(\angle{BOD})}{\sin(\angle{AOD})\sin(\angle{BOC})},4 KB (720 words) - 14:03, 26 January 2015
- In this solution, all lengths and angles are directed. ...\omega_C</math> intersect. We denote this point by <math>M.</math> Now, we angle chase:14 KB (1,830 words) - 17:22, 10 May 2023
- ...dinates of <math>P_1,P_2</math>, these will be continuous functions of the angle that <math>\pi</math> makes with <math>\pi_i</math>, and for one of the poi ...e <math>p_i</math> to the plane <math>p_j</math>. Similarly, we define the directed distance between two of a family of parallel lines in a plane.)7 KB (1,370 words) - 14:42, 29 January 2021
- ...Q</math> is inscribed in circle <math>\omega</math> with <math>\angle P = \angle Q = 90^{\circ}</math> and <math>AP = AQ < BP</math>. Let <math>X</math> be Let angle <math>\angle XAB=A</math>, which is an acute angle, <math>\tan{A}=t</math>, then <math>X=(1-a,at)</math>.5 KB (902 words) - 08:58, 20 August 2021
- ...</math> such that <math>\angle CBD=\angle YBA</math> and <math>\angle CDB=\angle YDA</math>. ...ot AD</math> composed with a reflection about the angle bisector of <math>\angle DAB</math> swaps the pairs <math>(D,B)</math> and <math>(C,X)</math>. Thus,2 KB (354 words) - 09:20, 23 April 2023
- ...math>AB = x</math>, <math>AC = y</math>, and <math>BC = z</math> and right angle at <math>A</math>. Let <math>ED = DF = x, AC = 5, \angle BAC = \alpha, \angle CDE = \beta. </math>22 KB (3,622 words) - 21:06, 10 October 2024