Triangles in Geometry

Triangle is one of the basic shapes in geometry. Triangle is defined as the 3 sided polygon. Based on the sides and angles the triangles are classified.

Equilateral triangle Right angle triangle Isosceles triangle Acute triangle Obtuse triangle Scalene Triangles

In this article we shall discuss about the various types of triangles and solving the angles of triangle. Solving Equilateral Triangles in Geometry:

All the sides and angles are equal. Such a triangle is called equilateral triangle.

Area of the equilateral triangle = `sqrt(3)/2 * a^2`

Right angle triangle in geometry:

One angle is exactly 90 degree and other two angles are less than 90 degree, such a triangle is called right angle triangle.

Area of right angle triangle = ½ * base * height

Isosceles triangle in geometry:

Two sides and angles are equals, such a triangle is called isosceles triangle.

Area of isosceles triangle = ½ * base * height

Acute triangle in geometry:

All angles are less than 90 degree, such a triangle is called acute triangle.

Obtuse triangle in geometry:

If any one of the angle is obtuse angle then it is more than 90 degree but less than 180 degree, such a triangle is called obtuse triangle.

Scalene triangle in geometry:

All the three sides and angles are unequal’s, such a triangle is called scalene triangle.

To find area of a scalene triangle, using the formula A = `sqrt(s(s-a)(s-b)(s-c))`

Where `s=(a+b+c)/2` a,b,c is the sides of triangle.

Note: Sum of the interior angles of any triangle is 180 degree Solving Angles of Triangles in Geometry:

Let us see how to solve the angles of triangle.

Find the third angle of the triangle whose angle is 66 degree and 34 degree.

Solution:

We know that sum of the interior angles of the triangle is 180 degree.

Let us take the unknown angle as x. 66+34+x=180

100 + x = 180

Subtract 100 on both sides.

100 + x - 100 = 180 - 100

X = 80

After solving the angles it becomes 66, 34 and 80 degree. Here, all the angles are less than 90 degree, so it’s an acute triangle.

Problems on solving angles of triangle:

Solve the right angle triangle whose one angle is 45 degree.Find the third angle and also find which type of triangle ?

Solution:

We know that, in right angle triangle one angle is 90 degree and in the given problem the another angle is 45 degree.

Sum of the interior angle of triangle = 180 degree.

Let us take the unknown angle is x,

x + 90 + 45 = 180

x + 135 = 180 Subtract 135 on both sides.

x + 135 - 135 = 180 - 135

x= 45 degree

Answer: After solving the third angle which is 45 degree, Since two angles are equal so it is an Isosceles. triangle.

Know more Corresponding Angles Definition i found this interesting link Center of a Circle

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