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:

- Acute Angle: Angles that lie between 0° to 90°.
- Obtuse Angle: Angles that lie between 90° to 180°
- Right Angle: An angle that is exactly equal to 90°
- Straight Angle: An angle that is exactly equal to 180°
- Reflex Angle: An angle that is greater than 180° but less than 360°
- Full Rotation: An angle that is exactly equal to 360°

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.

- An interior angle can be understood as the angles subtended by the arms of the figure or the lines inside the closed figure formed when the lines are joined to one another.
- Similarly, the
**exterior angle property**can be defined as the angles that are formed outside the closed figure or shape, between any side and line formed after extending the lines of the adjacent sides of that vertex.

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**:

- The sum of the interior angles of a triangle is 180 degrees.
- The sum of exterior angles of a triangle is 360 degrees.
- The sum of consecutive
**pairs of angles**, one interior and one exterior angle is 180 degrees. - The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

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.

**What do you mean by lines in geometry?**

A line in geometry can be defined as a straight set of points that extend in opposite directions and has a definite length but no defined width or breadth. It is a one-dimensional figure.

**What are angles in geometry?**

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 measure of angle is usually provided in degrees or radians. They are generally denoted using Greek letters such as θ, α, β.

**What is an obtuse angle in geometry?**

In geometry, an obtuse angle can be defined as an angle that measures greater than 90 degrees but is less than a straight angle or 180 degrees. For instance, 92 degrees, 175 degrees, 120 degrees are examples of obtuse angles.

**What is an exterior angle in geometry?**

An exterior angle can be defined as the angles that are formed outside the closed figure or shape. This angle is formed between any side of the closed figure and a line, formed after extending the lines of the adjacent sides of that vertex.

**What is a triangle in geometry?**

A triangle can be defined as a closed figure or regular 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.