BASIC GEOMETRY Lines and Angles 1 Introduction 2

BASIC GEOMETRY Ø Lines and Angles Ø 1. Introduction Ø 2. Point Ø 3. Plane Ø 4. Line Segment Ø 5. Ray Ø 6. Line Ø 7. Angles and its type

Ø 8. Ø Ø BASIC GEOMETRY Types of Angles (a) Supplementary Angles (b) Complementary Angles (c ) Adjacent Angles (d) Linear Pair Angles Ø 9. Measurement of Angles Ø 10. Perpendicular lines Ø 11. Perpendicular Bisector Ø 12. Angle Bisector

BASIC GEOMETRY ØThe word geometry is derived from the Greek word geometron , where geo means Earth and metron measurement Ø Point : - A sharp dot on a piece of paper made by the tip of a pencil or a pen is called a point. ØPLANE : - A plane is a flat two-dimensional (length and breadth) surface that extends infinitely in all directions. For example, the surface of a table, blackboard, wall, mirror and a piece of paper.

Line: A line is a collection of points extending indefinitely in both the directions along a straight path. It has no end points and no definite length

BASIC GEOMETRY . A . B In the figure given above, AB is a line. It is denoted by

BASIC GEOMETRY Line Segment: A line segment is a portion of a line. It has two end points. It has a definite length. It cannot be extended in any direction. It is the shortest distance between any two points. In the given figure. AB is a line segment. It is denoted by.

BASIC GEOMETRY Ray: A ray is also a part of a line that extends only in one direction. It has one end point ( called the initial point). It has no definite length. It cannot be measured. In the figure given below, AB is a ray. It is denoted by

BASIC GEOMETRY ANGLES : Two rays having the same initial point form an angle. An angle can also be formed when the lines or line segments meet or intersect each other at a point. Here ABC is an angle it is written as ∠ABC

BASIC GEOMETRY ØTypes of Angles – As per the measurement of an angle , angles are divided as follows Ø (1) Acute angle ( More than 00 and less than 900 ) Ø(2) Right angle ( Equal to 900 ) Ø(3) Obtuse angle ( More than 900 and less than 1800 ) Ø(4) Straight angle ( Equal to 1800 ) Ø(5) Reflex angle (More than 1800 and less than 3600 ) Ø(6) Complete angle ( Equal to 3600 )

BASIC GEOMETRY ØTypes of Angles – As per the measurement of an angle , angles are divided as follows (1) Acute angle : An angle whose measure is less than 90° is called an acute angle. In the figure shown alongside, ∠ABC forms an angle of 60° at vertex B. ( More than 00 and less than 900 ). So ∠ABC is an Acute Angle.

BASIC GEOMETRY (2) Right angle : - An angle whose measure is 90° is called a right angle. In the figure – ∠NOP forms 90° at vertex O. ∠NOP is a Right Angle. Here

BASIC GEOMETRY (3) Obtuse angle : - An angle whose measure is more than 90° but less than 180° is called an obtuse angle. In the figure given alongside, ∠ YOZ forms an angle of 150° at vertex 0. Here ∠XYZ is an Obtuse Angle.

BASIC GEOMETRY Ø Straight angle : An angle whose measure is 180° is called a straight angle. Ø In the figure - , ∠DOG is a straight angle.

BASIC GEOMETRY (5) Reflex angle : - An angle whose measure is more than 180° but lees than 360° is called a reflex angle. In the figure given - ∠ BOA forms an angle of 2200 at vertex 0. Here ∠BOA is a Reflex Angle.

BASIC GEOMETRY (6) Complete angle : - An angle whose measure is 360° is called a complete angle. In the figure - ∠POP forms an a Complete Angle.

BASIC GEOMETRY (7) Zero Angle : - An angle whose measure is 0° is called a zero angle. In the figure - ∠AOB forms an angle of 0° at the vertex 0. Here ∠AOB is a Zero Angle.

BASIC GEOMETRY Ø A sharp dot( • ) on a piece of paper showing a position or a location is called a point. Ø Two points join to form a line segment. Ø A line segment extending infinitely in both the directions is called a line. Ø A line segment extending infinitely in one direction is called a ray. Ø A smooth surface extending in all the directions is called a plane.

BASIC GEOMETRY Ø Two or more equidistant lines are called parallel lines. Ø More than two lines meeting each other at a point are called concurrent lines. Ø More than two points lying on the same line are called collinear points. Ø Two lines meeting each other at a point and forming a right angle are called perpendicular lines. Ø A line which divides a given angle into two equal parts is called an angle bisector.

BASIC GEOMETRY PROTECTOR

BASIC GEOMETRY