The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
A line in geometry is a one-dimensional figure with length but no breadth. It is formed when many points are extended linearly in opposite directions to any certain length extending upto infinity. On a two-dimensional plane, a line is defined by two points at the ends. These two points are also known as collinear points and lie on the same straight line.
In geometry, there are various kinds of lines, namely, horizontal lines, vertical lines, parallel lines and lines which are perpendicular to one another. These can be understood as the fundamental units of constructing any shape or polygon in geometry. For instance, a rectangle is made by joining four lines at the ends while a triangle is formed by three lines meeting at the ends.
In geometry, an angle is formed when two straight lines called rays or arms, are joined at a common point known as the vertex. The word angle is derived from the Latin word “Angulus”. The measure of angle is usually provided in degrees or radians. You can measure this using a protractor or a compass. They are generally denoted using Greek letters such as θ, α, β, and have three letter names where the centre mnemonic is for the vertex and the other two are for the arms of the angle formed.
Types of Angles
There are six main types of angles in mathematics. These have unique properties that are easy to understand. The list is as follows:
In a closed figure formed by the joining of extended points or lines, in geometry, there are at least 3 vertices where an angle is subtended inside of the figure. This figure can be any type of a shape or polygon including a triangle, pentagon, soiree, rhombus, etc. In all such geometrical 2D figures, there are interior angles and exterior angles.
For NCERT examinations, there are various types of two-dimensional closed figures that are tested. These shapes include triangles, squares, rectangles, quadrilaterals, parallelograms among other types of polygons.
In mathematics, a triangle can be defined as a closed figure or polygon with three sides. This shape or polygon consists of three edges and three vertices as well. And, the sum of all the internal angles in any triangle is equal to 180 degrees. This important property is called the angle sum property of triangles. The construction of simple triangles also needs this concept to be cleared. Moreover, if MOP is a triangle, then it is denoted as ∆MOP, where M, O and P are the three vertices of the triangle.
Properties of Triangles
Here are a few of the basic properties of triangles in geometry:
Geometry covers a range of topics such as shapes and figures, construction of simple triangles, 3D figures, angles and their properties, lines, among others. It is one of the most important branches in mathematics and it is one of the most scoring as well.