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LINES AND ANGLES CLASS 9 NOTES, Study notes of Mathematics

Mathematics

for students of class 9 notes for the chapter lines and angles

Typology: Study notes

2019/2020

Available from 05/26/2022

tvishi-upadhyay
tvishi-upadhyay 🇮🇳

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LINES AND ANGLES
CH- 6
NOTES
BASIC TERMS AND DEFINITION
Point
- A Point is that which has no component. It is represented by a dot.
Line
- When we join two distinct points then we get a line. A line has no endpoints that can be
extended infinitely.
Line Segment
- It is the part of the line which has two endpoints.
Ray
- Ray is also a part of the line which has only one endpoint and has no end on the
other side.
Collinear points
- Points lying on the same line are known as collinear points.
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LINES AND ANGLES

CH- 6

NOTES

BASIC TERMS AND DEFINITION

Point

  • A Point is that which has no component. It is represented by a dot. Line
  • When we join two distinct points then we get a line. A line has no endpoints that can be extended infinitely. Line Segment
  • It is the part of the line which has two endpoints. Ray
  • Ray is also a part of the line which has only one endpoint and has no end on the other side. Collinear points
  • Points lying on the same line are known as collinear points.

Non-collinear points

  • the points that don't lie on the same line are known as Non-Collinear Points Angles
  • When two rays begin from the same endpoint then they form an Angle. The two rays are the arms of the angle and the endpoint is the vertex of the angle.
  • Types of Angles: ANGLE NOTATION IMAGE Acute Between 0° and 90°. Right Exactly equal to 90° Obtuse Between 90° and 180° Reflex Between 180° and 360°

Vertically opposite Angles - two lines intersect each other at a point Intersecting Lines

  • The lines which cross each other from a particular point are called Intersecting Lines. Non-intersecting Lines
  • The lines which never cross each other at any point are called Non-intersecting Lines. Parallel Lines and a Transversal
  • If a line passes through two distinct lines and intersects them at distant points then this line is called aTransversal Line.
  • Here line “l” is transversal of line m and n. Exterior Angles
  • ∠1, ∠2, ∠7 and ∠ Interior Angles
  • ∠3, ∠4, ∠5 and ∠

Pairs of angles formed when a transversal intersects two lines- Corresponding angles Alternate interior angles Alternate exterior angles Interior angles on the same side of the transversal

  • ∠ 1 and ∠ 5
  • ∠ 2 and ∠ 6
  • ∠ 4 and ∠ 8
  • ∠ 3 and ∠ 7 - ∠ 4 and ∠ 6 - ∠ 3 and ∠ 5 - ∠ 1 and ∠ 7 - ∠ 2 and ∠ 8 - ∠ 4 and ∠ 5 - ∠ 3 and ∠ 6 AXIOMS AND THEOREMS Axioms
  • If a ray stands on a line, then the sum of two adjacent angles formed by that ray is 180°.
  • If the sum of two adjacent angles is 180°, then the arms which are not common of the angles form a line.
  • If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
  • If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other. Theorems
  • If two lines intersect each other, then the vertically opposite angles are equal
  • If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.