Types Of Triangles Geometric Figures

Triangles are a kind of polygons, having three sides that lie in one plane. All three angles of any triangle add up to 180º. According to the size of its angles, a triangle can be categorized as right-angle triangle, acute triangle and obtuse triangle. Another common classification for types of triangles is based on the lengths of the sides of a triangle. Examples of this type of classification are equilateral triangles, isosceles triangles and scalene triangles.

Amongst the various types of triangles is a triangle with one right angle (i.e. 90°) and it is known as a right-angle triangle. The side opposite to the right angle in a right-angle triangle is always the longest side of the triangle, and is called the hypotenuse. The remaining two sides are known as legs. The relation between the lengths of the sides of a right-angle triangle is demonstrated by the Pythagorean Theorem. The theorem is used to determine the length of the third side of a right angle triangle when the lengths of two sides are given. Let us assume the length of the hypotenuse as c and the length of the remaining sides as a and b. Thus according to Pythagoras theorem, c2 = a2 + b2.

Another triangle among the various types of triangles is a triangle with all angles acute (i.e. less than 90°) and it is known as an acute triangle. A triangle which has one obtuse angle (i.e. greater than 90º) is known as an obtuse triangle. The longest side of the triangle will always lie opposite the obtuse angle. A triangle with all three sides equal in length is called an equilateral triangle. All three angles of such a triangle are also equal, each measuring 60º.

One of the types of triangles, which have two sides of equal length, is known as an isosceles triangle. In such a triangle, the angles opposite the equal sides are also equal. A 3-4-5 triangle is a right triangle the lengths of whose sides are in the ratio of 3:4:5. Suppose you are provided with the lengths of two sides of a right triangle; check the ratio of the lengths to determine if the triangle falls in the 3:4:5 ratio. A 45°- 45°- 90° triangle is a special right triangle, with the three angles measuring 45°, 45°and 90°. The sides of a 45°- 45°- 90° triangle are of ratio of 1:1:2. Such a triangle can also be recognized by the angles. Suppose you are given that one of the angles in a right triangle measure to 45°. In such a case, you can easily surmise that since one of the angles in the triangle is 45°, the triangle must be a 45°- 45°- 90° special right angle triangle.Special right triangles