Lines Angles and Triangles Summary

Point

It is an exact location. It is a fine dot which has neither length nor breadth nor thickness but has position i.e., it has no magnitude. It is denoted by capital letters A, B, C, O etc.

Line segment

The straight path joining two points A and B is called a line segment

Ray

A line segment which can be extended in only one direction is called a ray.

Line

When a line segment is extended indefinitely in both directions it forms line.

Collinear points

If two or more points lie on the same line, then they are called collinear points.

Intersecting lines

Two lines having a common point are called intersecting lines. The common point is known as the point of intersection.

Concurrent lines

If two or more lines intersect at the same point, then they are known as concurrent lines.

Plane

A plane is a surface such that every point of the line joining any two points on it, lies on it.

• The line containing any two points in a plane lies wholly in that plane.

• An angle has only one and only one bisector.

• Through any point outside a line, one and only one perpendicular can be drawn to the given line.

• A segment has one and only one mid point.

• Linear pair postulate: If a ray stands on a line, then the sum of the two adjacent angles so formed is 180^o.

Angles

When two straight lines meet at a point they form an angle.

Types of Angles

Complementary and Supplementary angles

If the sum of the two angles is one right angle (i.e., 90^o), they are called complementary angles.

Supplementary angles

Two angles are said to be supplementary, if the sum of their measures is 180^o.

Vertically opposite angles

When two straight lines intersect each other at a point, the pairs of opposite angles so formed are called vertically opposite angles.