Page 61 - Ganit Kaushal

Summary of the Chapter

• Point: A point is an exact position or location on a plane surface. We indicate the position of a point by
placing a dot with a pencil. A point has no size, i.e., no width, length or depth.
• Line: A line is an infinitely thin, infinitely long collection of points extending in two opposite directions.
We use an arrow at each end to show that it extends infinitely.

It is denoted as AB and read as ‘Line AB’.
• Line segment: A line segment is a part of a line that is bounded by two distinct end points. A segment
is named by its two end points, written as AB and read as ‘Line segment AB’.
• Ray: A ray is a line that has one end point and goes on infinitely in only one
direction. The point where the ray starts is called the fixed end point. It is written

as AB. This is read as “ray AB”.
• Intersecting lines: A pair of lines that cut or cross each other at a single point are called intersecting
lines. The point where the intersecting lines meet is called the point of intersection.
• Parallel lines: Parallel lines are always the same distance apart and never touch. The symbol || is used
to denote parallel lines like l || m.
• Angle: An angle is made up of two rays with a common end point which is called the vertex of the
angle. The sides of the angle are called arms or legs of the angle. In specifying the angle, the vertex is
always written as the middle letter. We denote angle ABC as ∠ABC.

• Interior and Exterior of an angle: The plane of ∠ABC consists of three parts
associated with it.

(i) Interior of an angle: The shaded portion between the arms BA
and BC of the ∠ABC is called the interior of the angle. It extends
indefinitely.
(ii) Exterior of an angle: The part consisting of all those points that lie
outside the angle is called the exterior of the angle.
(iii) Boundary of an angle: The part consisting of all those points that lie
on the boundary of an angle.
In the given figure of ∠ABC, P is a point in the interior of ∠ABC, Q is a point
in the exterior of ∠ABC, and R is a point that lies on the boundary of the angle.
• Following is the classification of angles:

(i) Acute angle: An acute angle is an angle that is less than 90°.
(ii) Obtuse angle: An angle that is larger than 90° but smaller than 180° is called an obtuse
angle.

(iii) Right angle: An angle whose measure is 90° is called a right angle.
(iv) Straight angle: An angle whose measure is 180° is called a straight angle. A straight angle is
equal to two right angles.
(v) Reflex angle: An angle whose measure is more than 180° and less than 360° is called a reflex
angle.
• (i) The minute hand of a clock rotates through 360° in 60 minutes. That is 6° per minute.
(ii) The hour hand completes one complete revolution (i.e., 360°) in 12 hours.

∴ In one hour, a 360° ÷ 12 = 30° angle is made. In three hours, a 90° angle is made.

Lines and Angles 59