Equilateral triangles are polygons with equal sides and angles, each measuring 60 degrees. They possess unique properties such as congruent sides and angles, and their centers of mass, altitude, and circumcircle coincide. These triangles are fundamental in geometry, with practical uses in fields like architecture and engineering. Understanding their properties aids in calculating perimeter, area, and height, essential for various applications.
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Equilateral triangles are polygons with three equal sides and angles, and are a subset of regular polygons
Axes of Symmetry
Equilateral triangles have three axes of symmetry passing through each vertex
Concurrency of Centers
The centroid, orthocenter, circumcenter, and incenter all coincide at the same point within an equilateral triangle
All three sides and angles are congruent, and a perpendicular line from any vertex to the opposite side acts as an altitude, median, perpendicular bisector, and angle bisector
Each angle in an equilateral triangle is 60 degrees
A triangle is equilateral if and only if it is equiangular
The properties of equilateral triangles highlight the relationship between sides and angles in triangles
The perimeter of an equilateral triangle is three times the length of one side
The area of an equilateral triangle can be calculated using the formula (sqrt(3)/4)a^2
The height of an equilateral triangle can be found using the formula (sqrt(3)/2)a
Equilateral triangles have practical uses in fields such as architecture, engineering, and art
The properties and formulas of equilateral triangles can be applied to solve real-world problems and design challenges
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The term 'equilateral' is derived from Latin words 'aequus' and 'latus', which translate to '______' and '______' respectively.
equal
side
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Equilateral triangle side congruence
All three sides are equal in length.
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Equilateral triangle angle congruence
All three internal angles are 60 degrees.
