Calculate triangle sides, angles, area, perimeter with interactive diagram.
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A triangle is a polygon with three sides and three vertices. Each vertex is formed where two sides meet, and the triangle is commonly named using its vertices, such as △ABC.
Triangles can be classified by comparing the lengths of their sides. An equilateral triangle has three equal sides, an isosceles triangle has two equal sides, and a scalene triangle has no equal sides.
The lengths of a triangle’s sides are directly related to its internal angles. Equal sides always face equal angles.
Based on internal angles, triangles are classified as right or oblique. A right triangle has one angle equal to 90°, while oblique triangles are either acute or obtuse.
A triangle cannot have more than one angle that is greater than or equal to 90°. The sum of the internal angles of any triangle is always exactly 180°.
Additionally, the sum of the lengths of any two sides must always be greater than the length of the third side.
The Pythagorean theorem applies only to right triangles. It states that the square of the hypotenuse equals the sum of the squares of the other two sides.
The law of sines relates the sides of a triangle to the sines of their opposite angles. It is useful for finding unknown sides or angles.
If all three sides of a triangle are known, each angle can be calculated using inverse cosine functions.
There are multiple formulas for calculating the area of a triangle depending on the known values.
A median is a line segment drawn from a vertex to the midpoint of the opposite side. All three medians intersect at the centroid.
The inradius is the radius of the largest circle that fits inside the triangle. It is calculated using the triangle’s area and semiperimeter.
The circumradius is the radius of a circle that passes through all three vertices of the triangle.
No. A triangle can only have one right angle, otherwise the angle sum would exceed 180°.
No. Some right triangles, such as 45°–45°–90°, are isosceles.
Yes. Every triangle has a unique circumcircle.
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