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## Types of Triangles

A triangle is a polygon with three sides and three angles. The three angles of a triangle always add up to 180°. A triangle with vertices A, B, and C is denoted Δ ABC.

 Figure Type of Triangle Properties of Triangle Equilateral Triangle In an equilateral triangle, all sides are equal in length.  An equilateral triangle has all angles equal and measuring 60°. An equilateral triangle is also referred to as an equiangular triangle. Equilateral means 'equal sides', whereas equiangular means 'equal angles'. Isosceles Triangle In an isosceles triangle, two sides are equal in length. If two sides of a triangle are equal, then the angles opposite to them are equal (as per the isosceles triangle theorem in Euclidean geometry). Scalene Triangle In a scalene triangle, no two sides are equal in length. In a scalene triangle, all sides and internal angles are different from one another. Acute Triangle A triangle that has all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. Right Triangle A triangle that has an angle measuring 90° is a right triangle or right-angled triangle. The side opposite to the right angle is the hypotenuse. It is the longest side in the right triangle. The other two sides are called the legs of the right triangle. Obtuse Triangle A triangle that has one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle.

## Note

• An equilateral triangle is always an acute triangle because all its angles measure 60°.
• An isosceles triangle can be an acute triangle, or a right triangle (90° - 45° - 45°), or an obtuse triangle.
• A scalene triangle can be an acute triangle, or a right triangle, or an obtuse triangle.

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