Solving Geometry Expression

Introduction to solving geometry expression:

The word geometry is derived from the combination of two Greek words geo and Merton. The word geo and Merton combined to form the word geometry. Thus the subject of earth measurement was originally named as geometry. Later, Greeks emphasized the logical reasoning of geometrical facts and they dedicated their knowledge on geometry to the world of mathematics through the works of Pythagoras and Euclid. This culminated into the birth of the subject theoretical geometry.

Solving Geometry Expression-classifications:

Geometry has got many shapes and dimensions, let us discuss about the triangles.

Classification of the triangle in solving geometric expressions:

* Scalene triangle: When all the angles are different to one another then it is a scalene triangle.

* Isosceles triangle: When the angles opposite to the equal sides are equal, then it is an isosceles triangle

* Equilateral triangle: When all the angles are equal, then it is an equilateral triangle.

Classifying the angles of triangle in solving geometric expressions:

* Acute angled triangle

* Right angled triangle

* Obtuse angled triangle.

Solving Geometry Expression-illustrations:

Example 1:

Solving of geometric expression based on two angles of a triangle measure 55 and 85 and to find the measure of the third angle.

Solution:

Let the measure of third angle be X

We know that the sum, of the angles of a triangle is 180

55 + 85 + x = 180

Solving the expression we get,

140 + x = 180

X = 180 140

= 40

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Example 2:

Solving the geometric expression based on the ratio of the triangles

Let the angles of a triangle are in the ratio 2: 1: 3. Find the angles of a triangle.

Solution:

Let the angles of the given triangle be (2x) , x, (3x) .

We know that the sum, of the angles of a triangle is 180

2x + x + 3x =180

Solving the expression we get,

6x =180

X =180 / 6

= 30

2x = 2 * 30 = 60

x = 1 * 30 = 30

3x = 3 * 30 = 90

The angles of the triangle are 60, 30and 90.

by: Smith

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