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Triangle with at least two sides congruent
mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isosceles triangles have been used as decoration
Isosceles_triangle
Right triangle with a feature making calculations on the triangle easier
in their sides; see Triangle group. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right
Special_right_triangle
Geometric theorem about isosceles triangles
geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ˈpɒnz ˌæsɪˈnɔːrəm/
Pons_asinorum
Type of isosceles triangle
A golden triangle, also called a sublime triangle, is an isosceles triangle in which the duplicated side is in the golden ratio φ {\displaystyle \varphi
Golden_triangle_(mathematics)
Shape with three sides
different lengths is a scalene triangle. Isosceles triangle Equilateral triangle Scalene triangle Regarding the angles, a triangle in which one of the angles
Triangle
Property of geometry, also used to generalize the notion of "distance" in metric spaces
of any triangle. The first part is established using the lower figure. In the figure, consider the right triangle ADC. An isosceles triangle ABC is constructed
Triangle_inequality
Figure that, added to a given figure, makes a larger figure of the same shape
larger one. The gnomon is itself isosceles if and only if the ratio of the sides to the base of the original isosceles triangle, and the ratio of the base to
Gnomon_(figure)
Right triangle related to the golden ratio
same triangle characterize it in terms of the three Pythagorean means of two numbers, or via the inradius of isosceles triangles. This triangle is named
Kepler_triangle
Tetrahedron whose faces are all congruent
normally called a disphenoid. When the faces of a disphenoid are isosceles triangles, it is called a tetragonal disphenoid. In this case it has D 2 d
Disphenoid
Shape with three equal sides
occasionally known as the regular triangle. It is a special case of an isosceles triangle by modern definition. Its internal angle is 60 degrees or π/3 radians
Equilateral_triangle
In discrete geometry, an isosceles set is a set of points with the property that every three of them form an isosceles triangle. More precisely, each three
Isosceles_set
Number, approximately 1.618
triangle formed by two diagonals and a side of a regular pentagon is called a golden triangle or sublime triangle. It is an acute isosceles triangle with
Golden_ratio
December 5, 1995 —N/a Red isosceles triangle (based on the hoist side) dividing the flag into two right triangles; the upper triangle is green, the lower one
List of national flags of sovereign states
List_of_national_flags_of_sovereign_states
Small tiled plot of land in New York City
Village neighborhood of Manhattan in New York City. The plot is an isosceles triangle covered by a mosaic plaque that reads: PROPERTY OF THE HESS ESTATE
Hess_triangle
Asterism
Winter Triangle is an astronomical asterism formed from three of the brightest stars in the winter sky. It is an imaginary isosceles triangle drawn on
Winter_Triangle
fimbriated white isosceles triangle pointing towards hoist (unincorporated organized US territory) Flag of Antigua and Barbuda – an isosceles triangle pointing
List of national flags by design
List_of_national_flags_by_design
Triangle containing a 90-degree angle
right triangle is half of a rectangle which has been divided along its diagonal. When the rectangle is a square, its right-triangular half is isosceles, with
Right_triangle
Guinea is a horizontal tricolour of green, white, and red with a blue isosceles triangle based at the hoist and the coat of arms of Equatorial Guinea centered
Flag_of_Equatorial_Guinea
Topics referred to by the same term
up isosceles in Wiktionary, the free dictionary. An isosceles triangle is a triangle with two equal sides. Isosceles may also refer to: Isosceles (band)
Isosceles_(disambiguation)
and golden-yellow with white fimbriations and a red isosceles triangle at the hoist. The triangle is charged with a five-pointed gold star in its centre
Flag_of_Mozambique
Two-dimensional packing problem
isosceles right triangle". Retrieved 2011-05-01. Xu, Y. (1996). "On the minimum distance determined by n (≤ 7) points in an isoscele right triangle"
Circle packing in an isosceles right triangle
Circle_packing_in_an_isosceles_right_triangle
white fleurs de lis and a gold castle, respectively, and a white isosceles triangle at the hoist, within which is a gold five-pointed star. It was designed
Flag_of_Acadiana
Romantic relationship involving three people
of brotherhood and they allow a woman into their relationship, an isosceles triangle is created" automatically, as "in Truffaut's film Jules et Jim". René
Love_triangle
Unique positive real number which when multiplied by itself gives 2
also a right isosceles triangle. It also follows that FC = n − (m − n) = 2n − m. Hence, there is an even smaller right isosceles triangle, with hypotenuse
Square_root_of_2
Catalan solid with 60 faces
icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron. It has also been called
Triakis_icosahedron
side (and follow the flag's diagonals). The "Y" embraces a black isosceles triangle from which the arms are separated by narrow gold bands; the red and
Flag_of_South_Africa
Five-pointed star polygon
.} The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer
Pentagram
Line constructed from a triangle
line only for isosceles triangles, for which the Euler line coincides with the symmetry axis of the triangle and contains all triangle centers. The tangential
Euler_line
a cerulean blue field charged with a golden triangle in front of a white-edged black isosceles triangle. Adopted in 1967 to replace the British Blue
Flag_of_Saint_Lucia
Certain type of mistaken proof
isosceles triangle, from (Maxwell 1959, Chapter II, § 1), purports to show that every triangle is isosceles, meaning that two sides of the triangle are
Mathematical_fallacy
Trapezoid symmetrical about an axis
In Euclidean geometry, an isosceles trapezoid or isosceles trapezium is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides
Isosceles_trapezoid
Príncipe is a horizontal triband of green, yellow, and green, with a red isosceles triangle at the hoist and two five-pointed black stars on the yellow band.
Flag_of_São_Tomé_and_Príncipe
Shooting technique for handguns
Weaver stance. The Isosceles Stance is a two-handed technique in which the dominant hand's fingers grip the pistol directly (the Isosceles Grip is not recommended
Isosceles_Stance
the black isosceles triangle based on the hoist-side bearing a white five-pointed star in the center superimposed on the larger yellow triangle, also based
Flag_of_Timor-Leste
Special triangle in geometry
largest square that it contains, and is not the equilateral triangle. It is an isosceles triangle which is obtuse with an irrational but algebraic ratio between
Calabi_triangle
Near-miss Johnson solid with 92 faces
truncated icosahedron is a convex polyhedron. It has 92 faces: 60 isosceles triangles, 12 regular pentagons, and 20 regular hexagons. It is constructed
Rectified truncated icosahedron
Rectified_truncated_icosahedron
Marked objects for finding random numbers
starting from 6 Bipyramids, the duals of the infinite set of prisms, with triangle faces: any multiple of 4 (so that a facet faces up), starting from 8 Disphenoids
Dice
Triangles without a right angle
an isosceles triangle approaches 180°, and with the right inequality approaching equality only as the obtuse angle approaches 90°. If the triangle is
Acute_and_obtuse_triangles
Type of triangle
with. The skinny triangle finds uses in surveying, astronomy, and shooting. The approximated solution to the skinny isosceles triangle, referring to figure
Skinny_triangle
Property of objects which are scaled or mirrored versions of each other
isosceles triangles can have different base angles. If two angles of a triangle have measures equal to the measures of two angles of another triangle
Similarity_(geometry)
Tent function, often used in signal processing
a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often this is an isosceles triangle of
Triangular_function
seven-pointed stars and a white bordered blue isosceles triangle based on the hoist side with a shell inside the triangle. 2015 Proposed flag for Fiji A cyan field
Flag_of_Fiji
Triangle with integer side lengths
triangle is the building block for two isosceles Heronian triangles since the join can be along either leg. All pairs of isosceles Heronian triangles
Integer_triangle
bands sky blue and green, and a white isosceles triangle located on the side of the pole. In the middle of the triangle, a red five-pointed star appears.
Flag_of_Djibouti
Shape with ten sides
designated in the picture). Now the triangle E 10 E 1 P {\displaystyle {E_{10}E_{1}P}\;} is an isosceles triangle with vertex E 1 {\displaystyle E_{1}}
Decagon
Self-similar fractal curve
two sides of this triangle. At the second stage, the two new lines each form the base for another right-angled isosceles triangle, and are replaced by
Lévy_C_curve
Relation between sides of a right triangle
7289, calculates the diagonal of a square or, equivalently, of an isosceles right triangle. In India, the Baudhayana Shulba Sutra, the dates of which are
Pythagorean_theorem
tetragonal disphenoidal cells. Cells are face-transitive with 4 identical isosceles triangle faces. John Horton Conway calls it an oblate tetrahedrille or shortened
Tetragonal disphenoid honeycomb
Tetragonal_disphenoid_honeycomb
Geometrical theorem relating the lengths of two segments that divide a triangle
the theorem is that the angle bisector of the vertex angle of an isosceles triangle will also bisect the opposite side. There exist many different ways
Angle_bisector_theorem
by a red isosceles triangle based on the hoist-side pointed toward the fly-side and then divided into two right triangles. The upper triangle is green
Flag_of_Eritrea
does not go through its incenter unless the triangle is isosceles. For all non-isosceles triangles, the distance d from the incenter to the Euler line satisfies
List_of_triangle_inequalities
excircles of a triangle Inellipse Integer triangle Isodynamic point Isogonal conjugate Isoperimetric point Isosceles triangle Isosceles triangle theorem Isotomic
List_of_triangle_topics
On triangles inscribed in a circle with a diameter as an edge
OA = OB = OC, △OBA and △OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, ∠ OBC = ∠ OCB and ∠ OBA = ∠ OAB
Thales's_theorem
pall fesswise Argent, Azure, and Gules. The flag is formed from an isosceles triangle that extends halfway along the rectangle (a common mistake is to draw
Flag_of_the_Czech_Republic
Heronian triangle Pythagorean triangle Isosceles heronian triangle Primitive Heronian triangle Right triangle 30-60-90 triangle Isosceles right triangle Kepler
List of two-dimensional geometric shapes
List_of_two-dimensional_geometric_shapes
Perpendicular line segment from a triangle's side to opposite vertex
the triangle. The altitudes are also related to the sides of the triangle through the trigonometric functions. In an isosceles triangle (a triangle with
Altitude_(triangle)
1884 novella by Edwin Abbott Abbott
when dealing with Isosceles Triangles (Soldiers and Workmen) with only two congruent sides. The smallest angle of an Isosceles Triangle gains 30 arc minutes
Flatland
Small device used in playing guitar
metal, glass, tagua, or stone. They are often shaped in an acute isosceles triangle with the two equal corners rounded and the third corner less rounded
Guitar_pick
Four horizontal bands of yellow, white, red and blue and the green isosceles triangle is based on the hoist-side bearing the white vertical crescent moon
List_of_Arab_flags
Triangle center minimizing sum of distances to each vertex
construct an isosceles triangle, with base the side in question, 30-degree angles at the base, and the third vertex of each isosceles triangle lying outside
Fermat_point
13 polyhedra; duals of the Archimedean solids
(exact) Dihedral angle (approx.) Point group Triakis tetrahedron 12 isosceles triangles 18 8 arccos ( − 7 11 ) {\displaystyle \arccos(-{\frac {7}{11}})}
Catalan_solid
Polyhedron with 12 faces
resulting in ten triangles and two pentagons. It is C2v symmetry of order 4. Hexagonal bipyramid: a bipyramid with twelve isosceles triangles, obtained by
Dodecahedron
Specific, usually well-known application of a mathematical rule or law
case of the rhombus. If an isosceles triangle is defined as a triangle with at least 2 identical angles, an equilateral triangle is therefore a special case
Special_case
Geometric figure
and isosceles (30°, 30°, 120°) triangles. Within the figure, one side of a regular triangle coincides with one of the sides of an isosceles triangle, while
Spidron
Angle formed in the interior of a circle
both radii of the circle, so they have equal lengths. Therefore, triangle △VOA is isosceles, so angle ∠BVA and angle ∠VAO are equal. Angles ∠BOA and ∠AOV
Inscribed_angle
Near-cylindrical polyhedron with large area
limit of the areas of polyhedra. It is formed by stacked rings of isosceles triangles, arranged within each ring in the same pattern as an antiprism. The
Schwarz_lantern
Chemical compound
about 20% of the molecules were cyclic. The ring has C2v symmetry—an isosceles triangle—in contrast to the linear form that has equal N–N bond-lengths. Hansen
Trinitrogen
Generalization of Pythagorean theorem
a line segment of length b cos γ. Duplicate the right triangle to form the isosceles triangle ACP. Construct the circle with center A and radius b, and
Law_of_cosines
Species of beetle
noble chafer the scutellum is an equilateral triangle, but on the rose chafer it is an isosceles triangle. Rose chafers are capable of fast flight; they
Cetonia_aurata
Oval made by smoothly connecting four circular arcs
a right isosceles triangle ABC with apex C. To construct Moss's egg: Draw a semicircle on the base AB of the triangle, outside of the triangle. Connect
Moss's_egg
Catalan solid with 60 faces
edges equals 2 / ϕ {\displaystyle 2/\phi } . Its faces are acute isosceles triangles with one angle of arccos ( ( − 8 + 9 ϕ ) / 18 ) ≈ 68.618 720 931
Pentakis_dodecahedron
Concept in geometry
Euclid's Elements), forming an isosceles triangle. More generally, the law of sines states that the sine of each angle of a triangle is proportional to the side
Subtended_angle
English pastry
city of Coventry, England. They are in the form of a right-angled isosceles triangle, marked with three slits on the top and sprinkled with sugar. The
Coventry_Godcake
Quadrilateral symmetric across a diagonal
is tangent to its four sides at the four vertices of an isosceles trapezoid. For any isosceles trapezoid, tangent lines to the circumscribing circle at
Kite_(geometry)
Topics referred to by the same term
Golden triangle (composition), a rule of thumb for composition in photographs or paintings Golden triangle (mathematics), an isosceles triangle whose sides
Golden_Triangle
Point pair associated with plane triangles
These centers can be thought as the vertices of isosceles triangles erected on the sides of triangle ABC with the base angles equal to π/6 (30 degrees)
Napoleon_points
Paper model
(2007). "Octaflexagon: Isosceles Octaflexagon". Loki3.com. Retrieved October 26, 2012. Sherman, Scott (2007). "Enneaflexagon: Isosceles Enneaflexagon". Loki3
Flexagon
Mountain in the country of Canada
Isosceles Peak is a 2,488-metre (8,163-foot) mountain summit located in British Columbia, Canada. Isosceles Peak is set within Garibaldi Provincial Park
Isosceles_Peak
Ancient Greek philosopher (c. 626 – c. 545 BC)
a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. Two fundamental theorems
Thales_of_Miletus
Hungarian municipal flag
green isosceles triangles. It has been in effect since 15 September 2011, following a decree from the General Assembly of Budapest. The 11 triangles (6 red
Flag_of_Budapest
Pyramid with a square base
form of right pyramid with four isosceles triangles. When all of the pyramid's edges are equal in length, its triangles are all equilateral, an example
Square_pyramid
Special n-gon that has the largest area among all diameter-one n-gons
equidiagonal pentagon with an obtuse isosceles triangle attached to one of its sides, with the distance from the apex of the triangle to the opposite pentagon vertex
Biggest_little_polygon
Circumellipse of a triangle whose center is the triangle's centroid
S} and parallel to A B {\displaystyle AB} transforms the triangle onto the isosceles triangle A ′ B ′ C ′ {\displaystyle A'B'C'} (see diagram). Point C
Steiner_ellipse
Kepler–Poinsot polyhedron
broken into triangles, it is topologically related to the triakis icosahedron, with the same face connectivity, but much taller isosceles triangle faces. If
Great_stellated_dodecahedron
Cubic plane curve
the isosceles triangles is 1 2 ( π − θ ) {\displaystyle {\tfrac {1}{2}}(\pi -\theta )} . Segment F G {\displaystyle FG} divides the apex of isosceles triangle
Tschirnhausen_cubic
Theorem on cyclic quadrilateral
Finally, the angles ∠CME and ∠FMA are the same. Hence, △AFM is an isosceles triangle, and thus the sides AF and FM are equal. The proof that FD = FM goes
Brahmagupta_theorem
Polygon constructed from another
conversely. For example, the dual of a highly acute isosceles triangle is an obtuse isosceles triangle. In the Dorman Luke construction, each face of a dual
Dual_polygon
Polyhedron with parallel bases connected by triangles
right n-antiprisms have congruent regular n-gon bases and congruent isosceles triangle side faces, thus have the same (dihedral) symmetry group as the uniform
Antiprism
Type of metric space
is, every triple of points in the space forms an isosceles triangle, so the whole space is an isosceles set. Defining the (open) ball of radius r > 0 {\displaystyle
Ultrametric_space
Point on a line segment which is equidistant from both endpoints
triangle, the circumcenter is the midpoint of the hypotenuse. In an isosceles triangle, the median, altitude, and perpendicular bisector from the base side
Midpoint
Point in a triangle that can be seen as its middle under some criteria
components of the associated triangle center are always equal. Therefore, all triangle centers of an isosceles triangle must lie on its line of symmetry
Triangle_center
Geometry puzzle
form the problem was as follows: A B C {\displaystyle ABC} is an isosceles triangle with ∠ C B A = ∠ A C B = 80 ∘ . {\displaystyle \angle {CBA}=\angle
Langley's_Adventitious_Angles
Prism with a 3-sided base
the prism, two equilateral triangle faces on the planes of the triangular ends of the prism, and six more isosceles triangle faces. By giving rise to a
Triangular_prism
Polyhedron with 60 faces
dodecahedron - isosceles triangles Deltoidal hexecontahedron - kites Pentagonal hexecontahedron - pentagons Triakis icosahedron - isosceles triangles Concave
Hexecontahedron
Antiprism with 6-sided caps
can't be made uniform; the sides are isosceles triangles. Its vertex configuration is 3.3/2.3.6, with one triangle retrograde. It has D6d symmetry, order
Hexagonal_antiprism
Mathematical treatise by Euclid
and its converse (46–48). Proposition 5, that the base angles of an isosceles triangle are equal, became known in the Middle Ages as the pons asinorum, or
Euclid's_Elements
Triangle whose side lengths and area are integers
Examples of Heronian triangles that are not right-angled are the isosceles triangle obtained by joining a Pythagorean triangle and its mirror image along
Heronian_triangle
Line segment joining a triangle's vertex to the midpoint of the opposite side
vertex, and they all intersect at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex
Median_(geometry)
Solid made by joining an n- and 2n-gon with triangles and squares
many edges as the other, by an alternating band of isosceles triangles and rectangles. If the triangles are equilateral and the rectangles are squares, while
Cupola_(geometry)
Three tangent circles in a triangle
in area for an equilateral triangle is small, just over 1%, but as Howard Eves (1946) pointed out, for an isosceles triangle with a very sharp apex, the
Malfatti_circles
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ISOSCELES TRIANGLE
ISOSCELES TRIANGLE
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ISOSCELES TRIANGLE
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ISOSCELES TRIANGLE
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