Equilateral triangle - wikipedia Equilateral triangle `` Equilateral '' redirects here. For other uses, see Equilateral ( disambiguation ). Equilateral triangle Type Regular polygon Edges and vertices Schläfli symbol ( 3 ) Coxeter diagram Symmetry group Area 3 4 a 2 ( displaystyle ( \tfrac ( sqrt ( 3 ) ) ( 4 ) ) a ^ ( 2 ) ) Internal angle ( degrees ) 60 ° In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular ; that is, all three internal angles are also congruent to each other and are each 60 °. They are regular polygons, and can therefore also be referred to as regular triangles. Contents 1 Principal properties 2 Characterizations 2.1 Sides 2.2 Semiperimeter 2.3 Angles 2.4 Area 2.5 Circumradius, inradius and exradii 2.6 Equal cevians 2.7 Coincident triangle centers 2.8 Six triangles formed by partitioning by the medians 2.9 Points in the plane 3 Notable theorems 4 Other properties 5 Geometric construction 6 Derivation of area formula 6.1 Using the Pythagorean theorem 6.2 Using trigonometry 7 In culture and society 8 See also 9 References 10 External links Principal properties An equilateral triangle. It has equal sides ( a = b = c ), equal angles ( α = β = γ ( displaystyle alpha = \beta = gamma ) ), and equal altitudes ( h = h = h ). Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that : The area is A = 3 4 a 2 ( displaystyle A = ( \frac ( sqrt ( 3 ) ) ( 4 ) ) a ^ ( 2 ) ) The perimeter is p = 3 a ( displaystyle p = 3a , ! ) The radius of the circumscribed circle is R = a 3 ( displaystyle R = ( \frac ( a ) ( sqrt ( 3 ) ) ) ) The radius of the inscribed circle is r = 3 6 a ( displaystyle r = ( \frac ( sqrt ( 3 ) ) ( 6 ) ) a ) or r = R 2 ( displaystyle r = ( \frac ( R ) ( 2 ) ) ) The geometric center of the triangle is the center of the circumscribed and inscribed circles And the altitude ( height ) from any side is h = 3 2 a ( displaystyle h = ( \frac ( sqrt ( 3 ) ) ( 2 ) ) a ). Denoting the radius of the circumscribed circle as R, we can determine using trigonometry that : The area of the triangle is A = 3 3 4 R 2 ( displaystyle mathrm ( A ) = ( \frac ( 3 ( sqrt ( 3 ) ) ) ( 4 ) ) R ^ ( 2 ) ) Many of these quantities have simple relationships to the altitude ( `` h '' ) of each vertex from the opposite side : The area is A = h 2 3 ( displaystyle A = ( \frac ( h ^ ( 2 ) ) ( sqrt ( 3 ) ) ) ) The height of the center from each side, or apothem, is h 3 ( displaystyle ( \frac ( h ) ( 3 ) ) ) The radius of the circle circumscribing the three vertices is R = 2 h 3 ( displaystyle R = ( \frac ( 2h ) ( 3 ) ) ) The radius of the inscribed circle is r = h 3 ( displaystyle r = ( \frac ( h ) ( 3 ) ) ) In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors and the medians to each side coincide. Characterizations A triangle ABC that has the sides a, b, c, semiperimeter s, area T, exradii r, r, r ( tangent to a, b, c respectively ), and where R and r are the radii of the circumcircle and incircle respectively, is equilateral if and only if any one of the statements in the following nine categories is true. Thus these are properties that are unique to equilateral triangles. Sides a = b = c ( displaystyle displaystyle a = b = c ) a 2 + b 2 + c 2 = a b + b c + c a ( displaystyle displaystyle a ^ ( 2 ) + b ^ ( 2 ) + c ^ ( 2 ) = ab + bc + ca ) a b c = ( a + b − c ) ( a − b + c ) ( − a + b + c ) ( Lehmus ) ( displaystyle displaystyle abc = ( a + b-c ) ( a-b + c ) ( - a + b + c ) quad ( \text ( ( Lehmus ) ) ) ) ( a + b + c ) ( 1 a + 1 b + 1 c ) = 9 ( displaystyle displaystyle ( a + b + c ) ! left ( ( \frac ( 1 ) ( a ) ) + ( \frac ( 1 ) ( b ) ) + ( \frac ( 1 ) ( c ) ) \right ) = 9 ) 1 a + 1 b + 1 c = 25 R r − 2 r 2 4 R r ( displaystyle displaystyle ( \frac ( 1 ) ( a ) ) + ( \frac ( 1 ) ( b ) ) + ( \frac ( 1 ) ( c ) ) = ( \frac ( sqrt ( 25Rr - 2r ^ ( 2 ) ) ) ( 4Rr ) ) ) Semiperimeter s = 2 R + ( 3 3 − 4 ) r ( Blundon ) ( displaystyle displaystyle s = 2R+ ( 3 ( sqrt ( 3 ) ) - 4 ) r quad ( \text ( ( Blundon ) ) ) ) s 2 = 3 r 2 + 12 R r ( displaystyle displaystyle s ^ ( 2 ) = 3r ^ ( 2 ) + 12Rr ) s 2 = 3 3 T ( displaystyle displaystyle s ^ ( 2 ) = 3 ( sqrt ( 3 ) ) T ) s = 3 3 r ( displaystyle displaystyle s = 3 ( sqrt ( 3 ) ) r ) s = 3 3 2 R ( displaystyle displaystyle s = ( \frac ( 3 ( sqrt ( 3 ) ) ) ( 2 ) ) R ) Angles A = B = C = 60 ∘ ( displaystyle displaystyle A = B = C = 60 ^ ( circ ) ) cos ⁡ A + cos ⁡ B + cos ⁡ C = 3 2 ( displaystyle displaystyle cos ( A ) + cos ( B ) + cos ( C ) = ( \frac ( 3 ) ( 2 ) ) ) sin ⁡ A 2 sin ⁡ B 2 sin ⁡ C 2 = 1 8 ( displaystyle displaystyle sin ( \frac ( A ) ( 2 ) ) sin ( \frac ( B ) ( 2 ) ) sin ( \frac ( C ) ( 2 ) ) = ( \frac ( 1 ) ( 8 ) ) ) Area A = a 2 + b 2 + c 2 4 3 ( displaystyle displaystyle A = ( \frac ( a ^ ( 2 ) + b ^ ( 2 ) + c ^ ( 2 ) ) ( 4 ( sqrt ( 3 ) ) ) ) quad ) ( Weitzenböck ) A = 3 4 ( a b c ) 2 3 ( displaystyle displaystyle A = ( \frac ( sqrt ( 3 ) ) ( 4 ) ) ( abc ) ^ ( ^ ( \frac ( 2 ) ( 3 ) ) ) ) Circumradius, inradius and exradii R = 2 r ( Chapple - Euler ) ( displaystyle displaystyle R = 2r quad ( \text ( ( Chapple - Euler ) ) ) ) 9 R 2 = a 2 + b 2 + c 2 ( displaystyle displaystyle 9R ^ ( 2 ) = a ^ ( 2 ) + b ^ ( 2 ) + c ^ ( 2 ) ) r = r a + r b + r c 9 ( displaystyle displaystyle r = ( \frac ( r_ ( a ) + r_ ( b ) + r_ ( c ) ) ( 9 ) ) ) r a = r b = r c ( displaystyle displaystyle r_ ( a ) = r_ ( b ) = r_ ( c ) ) Equal cevians Three kinds of cevians are equal for ( and only for ) equilateral triangles : The three altitudes have equal lengths. The three medians have equal lengths. The three angle bisectors have equal lengths. Coincident triangle centers Every triangle center of an equilateral triangle coincides with its centroid, which implies that the equilateral triangle is the only triangle with no Euler line connecting some of the centers. For some pairs of triangle centers, the fact that they coincide is enough to ensure that the triangle is equilateral. In particular : A triangle is equilateral if any two of the circumcenter, incenter, centroid, or orthocenter coincide. It is also equilateral if its circumcenter coincides with the Nagel point, or if its incenter coincides with its nine - point center. Six triangles formed by partitioning by the medians For any triangle, the three medians partition the triangle into six smaller triangles. A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same inradius. A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid. Points in the plane A triangle is equilateral if and only if, for every point P in the plane, with distances p, q, and r to the triangle 's sides and distances x, y, and z to its vertices, 4 ( p 2 + q 2 + r 2 ) ≥ x 2 + y 2 + z 2. ( displaystyle 4 ( p ^ ( 2 ) + q ^ ( 2 ) + r ^ ( 2 ) ) geq x ^ ( 2 ) + y ^ ( 2 ) + z ^ ( 2 ). ) Notable theorems Morley 's trisector theorem states that, in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle. Napoleon 's theorem states that, if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those equilateral triangles themselves form an equilateral triangle. A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral. Viviani 's theorem states that, for any interior point P in an equilateral triangle with distances d, e, and f from the sides and altitude h, d + e + f = h, ( displaystyle d + e + f = h, ) independent of the location of P. Pompeiu 's theorem states that, if P is an arbitrary point in an equilateral triangle ABC, then there exists a triangle with sides of lengths PA, PB, and PC. That is, PA, PB, and PC satisfy the triangle inequality that any two of them sum to at least as great as the third. Other properties By Euler 's inequality, the equilateral triangle has the smallest ratio R / r of the circumradius to the inradius of any triangle : specifically, R / r = 2. The triangle of largest area of all those inscribed in a given circle is equilateral ; and the triangle of smallest area of all those circumscribed around a given circle is equilateral. The ratio of the area of the incircle to the area of an equilateral triangle, π 3 3 ( displaystyle ( \frac ( pi ) ( 3 ( sqrt ( 3 ) ) ) ) ), is larger than that of any non-equilateral triangle. The ratio of the area to the square of the perimeter of an equilateral triangle, 1 12 3, ( displaystyle ( \frac ( 1 ) ( 12 ( sqrt ( 3 ) ) ) ), ) is larger than that for any other triangle. If a segment splits an equilateral triangle into two regions with equal perimeters and with areas A and A, then 7 9 ≤ A 1 A 2 ≤ 9 7. ( displaystyle ( \frac ( 7 ) ( 9 ) ) leq ( \frac ( A_ ( 1 ) ) ( A_ ( 2 ) ) ) leq ( \frac ( 9 ) ( 7 ) ). ) If a triangle is placed in the complex plane with complex vertices z, z, and z, then for either non-real cube root ω ( displaystyle omega ) of 1 the triangle is equilateral if and only if z 1 + ω z 2 + ω 2 z 3 = 0. ( displaystyle z_ ( 1 ) + omega z_ ( 2 ) + omega ^ ( 2 ) z_ ( 3 ) = 0. ) Given a point P in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when P is the centroid. In no other triangle is there a point for which this ratio is as small as 2. This is the Erdős -- Mordell inequality ; a stronger variant of it is Barrow 's inequality, which replaces the perpendicular distances to the sides with the distances from P to the points where the angle bisectors of ∠ APB, ∠ BPC, and ∠ CPA cross the sides ( A, B, and C being the vertices ). For any point P in the plane, with distances p, q, and t from the vertices A, B, and C respectively, 3 ( p 4 + q 4 + t 4 + a 4 ) = ( p 2 + q 2 + t 2 + a 2 ) 2. ( displaystyle displaystyle 3 ( p ^ ( 4 ) + q ^ ( 4 ) + t ^ ( 4 ) + a ^ ( 4 ) ) = ( p ^ ( 2 ) + q ^ ( 2 ) + t ^ ( 2 ) + a ^ ( 2 ) ) ^ ( 2 ). ) For any point P on the inscribed circle of an equilateral triangle, with distances p, q, and t from the vertices, 4 ( p 2 + q 2 + t 2 ) = 5 a 2 ( displaystyle displaystyle 4 ( p ^ ( 2 ) + q ^ ( 2 ) + t ^ ( 2 ) ) = 5a ^ ( 2 ) ) and 16 ( p 4 + q 4 + t 4 ) = 11 a 4. ( displaystyle displaystyle 16 ( p ^ ( 4 ) + q ^ ( 4 ) + t ^ ( 4 ) ) = 11a ^ ( 4 ). ) For any point P on the minor arc BC of the circumcircle, with distances p, q, and t from A, B, and C respectively, p = q + t ( displaystyle displaystyle p = q + t ) and q 2 + q t + t 2 = a 2 ; ( displaystyle displaystyle q ^ ( 2 ) + qt + t ^ ( 2 ) = a ^ ( 2 ) ; ) moreover, if point D on side BC divides PA into segments PD and DA with DA having length z and PD having length y, then z = t 2 + t q + q 2 t + q, ( displaystyle z = ( \frac ( t ^ ( 2 ) + tq + q ^ ( 2 ) ) ( t + q ) ), ) which also equals t 3 − q 3 t 2 − q 2 ( displaystyle ( \tfrac ( t ^ ( 3 ) - q ^ ( 3 ) ) ( t ^ ( 2 ) - q ^ ( 2 ) ) ) ) if t ≠ q ; and 1 q + 1 t = 1 y, ( displaystyle ( \frac ( 1 ) ( q ) ) + ( \frac ( 1 ) ( t ) ) = ( \frac ( 1 ) ( y ) ), ) which is the optic equation. There are numerous triangle inequalities that hold with equality if and only if the triangle is equilateral. An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. Its symmetry group is the dihedral group of order 6 D. Equilateral triangles are the only triangles whose Steiner inellipse is a circle ( specifically, it is the incircle ). A regular tetrahedron is made of four equilateral triangles. Equilateral triangles are found in many other geometric constructs. The intersection of circles whose centers are a radius width apart is a pair of equilateral arches, each of which can be inscribed with an equilateral triangle. They form faces of regular and uniform polyhedra. Three of the five Platonic solids are composed of equilateral triangles. In particular, the regular tetrahedron has four equilateral triangles for faces and can be considered the three - dimensional analogue of the shape. The plane can be tiled using equilateral triangles giving the triangular tiling. Geometric construction Construction of equilateral triangle with compass and straightedge An equilateral triangle is easily constructed using a compass and straightedge, as 3 is a Fermat prime. Draw a straight line, and place the point of the compass on one end of the line, and swing an arc from that point to the other point of the line segment. Repeat with the other side of the line. Finally, connect the point where the two arcs intersect with each end of the line segment An alternative method is to draw a circle with radius r, place the point of the compass on the circle and draw another circle with the same radius. The two circles will intersect in two points. An equilateral triangle can be constructed by taking the two centers of the circles and either of the points of intersection. In both methods a by - product is the formation of vesica piscis. The proof that the resulting figure is an equilateral triangle is the first proposition in Book I of Euclid 's Elements. Derivation of area formula The area formula A = 3 4 a 2 ( displaystyle A = ( \frac ( sqrt ( 3 ) ) ( 4 ) ) a ^ ( 2 ) ) in terms of side length a can be derived directly using the Pythagorean theorem or using trigonometry. Using the Pythagorean theorem The area of a triangle is half of one side a times the height h from that side : A = 1 2 a h. ( displaystyle A = ( \frac ( 1 ) ( 2 ) ) ah. ) An equilateral triangle with a side of 2 has a height of √ 3 as the sine of 60 ° is √ 3 / 2. The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base a, and the hypotenuse is the side a of the equilateral triangle. The height of an equilateral triangle can be found using the Pythagorean theorem ( a 2 ) 2 + h 2 = a 2 ( displaystyle left ( ( \frac ( a ) ( 2 ) ) \right ) ^ ( 2 ) + h ^ ( 2 ) = a ^ ( 2 ) ) so that h = 3 2 a. ( displaystyle h = ( \frac ( sqrt ( 3 ) ) ( 2 ) ) a. ) Substituting h into the area formula ( 1 / 2 ) ah gives the area formula for the equilateral triangle : A = 3 4 a 2. ( displaystyle A = ( \frac ( sqrt ( 3 ) ) ( 4 ) ) a ^ ( 2 ). ) Using trigonometry Using trigonometry, the area of a triangle with any two sides a and b, and an angle C between them is A = 1 2 a b sin ⁡ C. ( displaystyle A = ( \frac ( 1 ) ( 2 ) ) ab sin C. ) Each angle of an equilateral triangle is 60 °, so A = 1 2 a b sin ⁡ 60 ∘. ( displaystyle A = ( \frac ( 1 ) ( 2 ) ) ab sin 60 ^ ( circ ). ) The sine of 60 ° is 3 2 ( displaystyle ( \tfrac ( sqrt ( 3 ) ) ( 2 ) ) ). Thus A = 1 2 a b × 3 2 = 3 4 a b = 3 4 a 2 ( displaystyle A = ( \frac ( 1 ) ( 2 ) ) ab \times ( \frac ( sqrt ( 3 ) ) ( 2 ) ) = ( \frac ( sqrt ( 3 ) ) ( 4 ) ) ab = ( \frac ( sqrt ( 3 ) ) ( 4 ) ) a ^ ( 2 ) ) since all sides of an equilateral triangle are equal. In culture and society Equilateral triangles have frequently appeared in man made constructions : Some archaeological sites have equilateral triangles as part of their construction, for example Lepenski Vir in Serbia. The shape also occurs in modern architecture such as Randhurst Mall and the Jefferson National Expansion Memorial. The Flag of Nicaragua, the Flag of the Philippines, the Seal of the President of the Philippines, and the Flag of Junqueirópolis contain equilateral triangles. It is a shape of a variety of road signs, including the Yield sign. The fraternity Tau Kappa Epsilon uses the equilateral triangle as its primary symbol. See also Almost - equilateral Heronian triangle Isosceles triangle Right triangle Trigonometry Ternary plot References ^ Jump up to : Andreescu, Titu ; Andrica, Dorian ( 2006 ). Complex Numbers from A to... Z. Birkhäuser. pp. 70, 113 -- 115. ^ Jump up to : Pohoata, Cosmin ( 2010 ). `` A new proof of Euler 's inradius - circumradius inequality '' ( PDF ). Gazeta Matematica Seria B ( 3 ) : 121 -- 123. Jump up ^ ( 1 ) Jump up ^ Bencze, Mihály ; Wu, Hui - Hua ; Wu, Shan - He ( 2008 ). `` An equivalent form of fundamental triangle inequality and its applications '' ( PDF ). Research Group in Mathematical Inequalities and Applications. 11 ( 1 ). Jump up ^ Dospinescu, G. ; Lascu, M. ; Pohoata, C. ; Letiva, M. ( 2008 ). `` An elementary proof of Blundon 's inequality '' ( PDF ). Journal of inequalities in pure and applied mathematics. 9 ( 4 ). Jump up ^ Blundon, W.J. ( 1963 ). `` On Certain Polynomials Associated with the Triangle ''. Mathematics Magazine. 36 ( 4 ) : 247 -- 248. doi : 10.2307 / 2687913. ^ Jump up to : Alsina, Claudi ; Nelsen, Roger B. ( 2009 ). When less is more. Visualizing basic inequalities. Mathematical Association of America. pp. 71, 155. Jump up ^ McLeman, Cam ; Ismail, Andrei. `` Weizenbock 's inequality ''. PlanetMath. Archived from the original on 2012 - 02 - 18. Jump up ^ Owen, Byer ; Felix, Lazebnik ; Deirdre, Smeltzer ( 2010 ). Methods for Euclidean Geometry. Mathematical Association of America. pp. 36, 39. Jump up ^ Yiu, Paul ( 1998 ). `` Notes on Euclidean Geometry '' ( PDF ). ^ Jump up to : Cerin, Zvonko ( 2004 ). `` The vertex - midpoint - centroid triangles '' ( PDF ). Forum Geometricorum. 4 : 97 -- 109. ^ Jump up to : `` Inequalities proposed in `` Crux Mathematicorum '' '' ( PDF ). ^ Jump up to : Chakerian, G.D. `` A Distorted View of Geometry. '' Ch. 7 in Mathematical Plums ( R. Honsberger, editor ). Washington, DC : Mathematical Association of America, 1979 : 147. ^ Jump up to : Posamentier, Alfred S. ; Salkind, Charles T. ( 1996 ). Challenging Problems in Geometry. Dover Publ. Jump up ^ Svrtan, Dragutin ; Veljan, Darko ( 2012 ). `` Non-Euclidean versions of some classical triangle inequalities '' ( PDF ). Forum Geometricorum. 12 : 197 -- 209. Jump up ^ Dörrie, Heinrich ( 1965 ). 100 Great Problems of Elementary Mathematics. Dover Publ. pp. 379 -- 380. Jump up ^ Minda, D. ; Phelps, S. ( 2008 ). `` Triangles, ellipses, and cubic polynomials ''. American Mathematical Monthly. 115 ( October ) : 679 -- 689. Jump up ^ Dao, Thanh Oai ( 2015 ). `` Equilateral triangles and Kiepert perspectors in complex numbers '' ( PDF ). Forum Geometricorum. 15 : 105 -- 114. Jump up ^ Lee, Hojoo ( 2001 ). `` Another proof of the Erdős -- Mordell Theorem '' ( PDF ). Forum Geometricorum. 1 : 7 -- 8. ^ Jump up to : De, Prithwijit ( 2008 ). `` Curious properties of the circumcircle and incircle of an equilateral triangle ''. Mathematical Spectrum. 41 ( 1 ) : 32 -- 35. External links Weisstein, Eric W. `` Equilateral Triangle ''. MathWorld. Polygons Special cases, including regular polygons with their own names, in parentheses List of polygons by number of sides 1 -- 10 sides Monogon Digon Triangle Equilateral Isosceles Quadrilateral Square Rectangle Rhombus Parallelogram Trapezoid Kite Pentagon Hexagon Heptagon Octagon Nonagon ( Enneagon ) Decagon 11 -- 20 sides Hendecagon Dodecagon Tridecagon Tetradecagon Pentadecagon Hexadecagon Heptadecagon Octadecagon Enneadecagon Icosagon 21 -- 100 sides ( selected ) Icositetragon ( 24 ) Triacontagon ( 30 ) Triacontadigon ( 32 ) Triacontatetragon ( 34 ) Tetracontagon ( 40 ) Tetracontadigon ( 42 ) Tetracontaoctagon ( 48 ) Pentacontagon ( 50 ) Hexacontagon ( 60 ) Hexacontatetragon ( 64 ) Heptacontagon ( 70 ) Octacontagon ( 80 ) Enneacontagon ( 90 ) Enneacontahexagon ( 96 ) Hectogon ( 100 ) > 100 sides 120 - gon 257 - gon 360 - gon Chiliagon ( 1,000 ) Myriagon ( 10,000 ) 65537 - gon Megagon ( 1,000,000 ) Apeirogon ( ∞ ) Star polygons ( 5 -- 12 sides ) Pentagram Hexagram Heptagram Octagram Enneagram Decagram Hendecagram Dodecagram Fundamental convex regular and uniform polytopes in dimensions 2 -- 10 Family I ( p ) / D E / E / E / E / E / F / G Regular polygon Triangle Square p - gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron Cube Demicube Dodecahedron Icosahedron Uniform 4 - polytope 5 - cell 16 - cell Tesseract Demitesseract 24 - cell 120 - cell 600 - cell Uniform 5 - polytope 5 - simplex 5 - orthoplex 5 - cube 5 - demicube Uniform 6 - polytope 6 - simplex 6 - orthoplex 6 - cube 6 - demicube 1 2 Uniform 7 - polytope 7 - simplex 7 - orthoplex 7 - cube 7 - demicube 1 2 3 Uniform 8 - polytope 8 - simplex 8 - orthoplex 8 - cube 8 - demicube 1 2 4 Uniform 9 - polytope 9 - simplex 9 - orthoplex 9 - cube 9 - demicube Uniform 10 - polytope 10 - simplex 10 - orthoplex 10 - cube 10 - demicube Uniform n - polytope n - simplex n - orthoplex n - cube n - demicube 1 2 k n - pentagonal polytope Topics : Polytope families Regular polytope List of regular polytopes and compounds Retrieved from `` https://en.wikipedia.org/w/index.php?title=Equilateral_triangle&oldid=806227710 '' Categories : Triangles Triangle geometry Elementary shapes Constructible polygons Hidden categories : All articles with dead external links Articles with dead external links from September 2017 Articles with permanently dead external links Talk Contents About Wikipedia Azərbaycanca Български Boarisch Bosanski Català Чӑвашла Čeština ChiShona Corsu Dansk Davvisámegiella Deutsch Eesti Ελληνικά Español Esperanto Euskara فارسی Français 한국어 हिन्दी Hornjoserbsce Hrvatski Bahasa Indonesia Íslenska Italiano עברית ქართული Қазақша Latviešu Lëtzebuergesch Македонски മലയാളം मराठी Bahasa Melayu Nederlands नेपाली 日本 語 Norsk Norsk nynorsk ភាសា ខ្មែរ Polski Português Română Русский Scots Simple English Slovenčina Slovenščina Ślůnski کوردی Српски / srpski Srpskohrvatski / српскохрватски Suomi Svenska தமிழ் తెలుగు ไทย Türkçe Українська Tiếng Việt West - Vlams 粵語 中文 Edit links This page was last edited on 20 October 2017, at 15 : 57. 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Question: how many lines of symmetry has an equilateral triangle
Answer: 3 lines of reflection and rotational symmetry of order 3 about its center