A triangle or trigon is a two dimensional geometric object that has the specific qualities of having three straight sides that intersect at three vertices.

The sum of the internal angles that exist at the vertices always total the same number for every triangle—180 degrees, or π radians.

In Euclidean geometry, any three non-collinear points determine a unique triangle and a unique plane.

Types of triangles

By relative lengths of sides

Triangles can be classified according to the relative lengths of their sides:

In an equilateral triangle, all sides are the same length. An equilateral triangle is also a regular polygon with all angles 60°.

In an isosceles triangle, at least two sides are equal in length. An isosceles triangle also has two equal angles: the angles opposite the two equal sides.

In a scalene triangle, all sides and internal angles are different from one another.

By internal angles

Triangles can also be classified according to their internal angles, measured here in degrees.

A triangle that does not contain a right angle is called an oblique triangle. One that does is a right triangle.

There are two types of oblique triangles, those with all the internal angles smaller than 90°, and those with one angle larger than 90°.

The obtuse triangle contains the larger than 90° angle, known as an obtuse angle. The acute triangle is composed of three acute angles, the same as saying that all three of its angles are smaller than 90°.

A right triangle (or right-angled triangle) has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle. Right triangles conform to the Pythagorean theorem: the sum of the squares of the two legs is equal to the square of the hypotenuse; i.e., a2 + b2 = c2, where a and b are the legs and c is the hypotenuse

The sum of the internal angles that exist at the vertices always total the same number for every triangle—180 degrees, or π radians.

In Euclidean geometry, any three non-collinear points determine a unique triangle and a unique plane.

Types of triangles

By relative lengths of sides

Triangles can be classified according to the relative lengths of their sides:

In an equilateral triangle, all sides are the same length. An equilateral triangle is also a regular polygon with all angles 60°.

In an isosceles triangle, at least two sides are equal in length. An isosceles triangle also has two equal angles: the angles opposite the two equal sides.

In a scalene triangle, all sides and internal angles are different from one another.

By internal angles

Triangles can also be classified according to their internal angles, measured here in degrees.

**Download Theory of Mathematics UN according to grid UN 2010/2011****Download the sample of Questions**A triangle that does not contain a right angle is called an oblique triangle. One that does is a right triangle.

There are two types of oblique triangles, those with all the internal angles smaller than 90°, and those with one angle larger than 90°.

The obtuse triangle contains the larger than 90° angle, known as an obtuse angle. The acute triangle is composed of three acute angles, the same as saying that all three of its angles are smaller than 90°.

A right triangle (or right-angled triangle) has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle. Right triangles conform to the Pythagorean theorem: the sum of the squares of the two legs is equal to the square of the hypotenuse; i.e., a2 + b2 = c2, where a and b are the legs and c is the hypotenuse

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