Equilateral Triangle
From Latin: aequus -"equal" , latus -"side"
A triangle which has all three of its sides equal in length.
Try this Drag the orange dots on each vertex to reshape the triangle.
Notice it always remains an equilateral triangle. The sides AB, BC and AC always remain equal in length
(If there is no image below, see support page.)
An equilateral triangle is simply a specific case of a regular polygon, in this case with 3 sides.
All the facts and properties described for regular polygons apply to an equilateral triangle.
See Regular Polygons
Properties
- All three angles of an equilateral triangle are always 60°.
In the figure above, the angles ∠ABC, ∠CAB and
∠ACB are always the same.
Since the angles are the same and the internal angles of any triangle always add to 180°, each is 60°.
- The area of an equilateral triangle can be calculated in the
usual way,
but in this special case of an equilateral triangle, it is also given by the formula:
where S is the length of any one side.
- In the case of an equilateral triangle, the radius of the
incircle is exactly half the radius of the
circumcircle.
Things to Ponder
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Can an equilateral triangle also be isosceles?
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answer
Yes. Always. An isosceles triangle has at least two sides equal, and an equilateral triangle has all 3 sides equal
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Can an equilateral triangle also be a right triangle?
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answer
No. By definition a right triangle has one interior angle = 90° . An equilateral triangle's are always all 60°
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What is the area of an equilateral triangle with each side 10 inches long?
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answer
Somewhere between 41.1 and 44.9 sq inches
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Challenge question: What is the radius of the incircle of an equilateral triangle which has each side 10 km long?
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answer
Somewhere between 2.8 and 3.1 km
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Constructing an Equilateral Triangle
It is possible to construct an equilateral triangle of a given side length using just a compass and straightedge. See
Constructing an Equilateral Triangle
Related triangle topics
General
Triangle types
Triangle centers
Congruence and Similarity
Triangle quizzes and exercises
(C) 2007 Copyright John Page
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