Download Formula And Definitions Of Lines And Angles Class 9 NCERT CBSE Download In Pdf

Chapter 6 Lines and Angles Class 9 NCERT CBSE Download in Pdf

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(1)** Point** - We often represent a point by a fine dot made with a fine sharpened pencil on a piece of paper.

(2) **Line -** A line is completely known if we are given any two distinct points. Line AB is represented by asÂ . A line or a straight line extends indefinitely in both the directions

(3) **Line segment -** A part (or portion) of a line with two end points is called a line segment.

(4) **Ray - **A part of line with one end point is called a ray.

(5) **Collinear points -** If three or more points lie on the same line, they are called
collinear points otherwise they are called non-collinear points.

**T****y****pes of Angles -**

(1)**Acute angle - **An acute angle measure between 0^{o} and 90^{o
}(2) **Right angle - **A right angle is exactly equal to 90^{o}.

(3)**Obtuse angle - **An angle greater than 90^{o} but less than 180^{o}

(4 )**Straight angle - **A straight angle is equal to 180^{o}.

(5)**Reflex angle - **An angle which is greater than 180^{o} but less than 360^{o} is called a reflex angle.

(6)**ComplementaryÂ anglesÂ - **Two angles whoseÂ sumÂ isÂ 90^{o} areÂ called complementary angles.

(7)**SupplementaryÂ angleÂ - **TwoÂ anglesÂ whoseÂ sumÂ iisÂ 180 are called supplementary angles.

(8)**Adjacent angles - **Two angles are adjacent, if they have a common vertex, a common arm and their non common arms are on different sides of common arm.

(9)**Linear pair - **Two angles form a linear pair, if their non-common arms form a line.

(10)**Vertically opposite angles** - Vertically opposite angles are formed when two lines intersect each other at a point.

**TRANSVERSAL**

(a) Corresponding angles

(b) Alternate interior angles

(c) Alternate exterior angles

(d) Interior angles on the same side of the transversal.

â€¢If a transversal intersects two parallel lines, then

(i) each pair of corresponding angles is equal.

(ii) each pair of alternate interior angles is equal.

(iii) each pair of interior Â angle Â on Â the Â same Â side Â of Â the Â transversal Â is supplementary.

â€¢Â If a transversal interacts two lines such that, either

(i) any one pair of corresponding angles is equal, or

(ii) any one pair of alternate interior angles is equal or

(iii) any one pair of interior angles on the same side of he transversal Â is supplementary then the lines are parallel.

â€¢Â Lines which are parallel to a given line are parallel to each other.

â€¢Â The sum of the three angles of a triangle is 180^{o}.

â€¢Â If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

Q.1Â In the given figure, The value of y is

(a)10^{o}

(b)40^{o}

(c) 36^{o}

(d) 45^{o}

Q.2Â An exterior angle of a triangle is 750 Â and its two interior opposite angles are equal. Each of these equal angles is

(a) 105^{o}

Â (b) 50.5^{o}Â

(c) 52^{o}Â

(d) 37.5^{o}

Q.3Â The compliment of an angle 'm' is:

(a) m

(b) 90^{o}+m

(c) 90^{o}-m

(d)mÂ Ã—90^{o}

Q.4If one angle of a triangle is equal to the sum of the other two equal angles, then the triangle is

(a) an isosceles triangle

(b)an obtuse triangle

(c)an equilateral triangle

(d) a right triangle

Q.5 In the given figure form a linear pair if a-b = 100^{o }then a and b are

(a)120^{o}, 20^{o}Â

(b) 40^{o}, 140^{o}

(c) 50^{o}, 150^{o}Â

(d) 140^{o}, 40^{o}

Q.6Â Angle of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is

(a) 60^{o}

(b) 40^{o}Â

(c) 80^{o}Â

(d) 20^{o}

**Section - B**

Q.7Â Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

Q.8Â In the following figures which of the two lines are parallel and why?

(i)Â Â Â Â (ii)

Q.10 Â In the fig.

Q.11 Sum of two angles of a triangle is 90^{o} Â and their difference is 50^{o}. Find all the angles of the triangle.

Q.12 Â In the adjoining figure, .

**Section - C**

Q.13 Â In the given figure AB and CD intersect each other at O. IfÂ Â find the value of x,y and z.

Q.14 Â Prove that vertically opposite angle are equal.

Q.15 Â In the given figureÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Q.16 Â In the given figureÂ are bisectors respectively find

Q.17 Â The angles of a triangle are in the ratio 2: 3: 5 find the angles of the triangle.

Q.18 Â Find x and y in the following figure.

Q.19 Â In figure find x.

**Section - D**

Q.20 Prove that sum of the angles of triangle is 180^{o}.

Q.21 Prove that sum of the angles of a hexagon is 720^{o}.

Q.22 The angles of a triangle are find the value of x.

Q.23 In the given figure, AD and CE are the angle bisectors of respectively If

Q.24 Â A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angle so formed are parallel.

Answer :

(1) b

(2) dÂ

(3) c

(4) a,d

( 5) d

(6) b

(9) 65^{o}

(10) 115^{o
}(11) 20^{o}, 70^{o}, 90^{o}

(12) 95^{o
}(13) 84^{o}, 21^{o}, 48^{o
}(16)90^{o}

(17) 36^{o}, 54^{o}, 90^{o}Â

(18) 48^{o}, 12^{o}Â

(19) 30^{o
}(22) 100^{o}

(23) 135^{o}

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- Chapter 1 NUMBER SYSTEMS
- Chapter 2 POLYNOMIALS
- Chapter 3 COORDINATE GEOMETRY
- Chapter 5 INTRODUCTION TO EUCLIDâ€™S GEOMETRY
- Chapter 6 LINES AND ANGLES
- Chapter 7 TRIANGLES
- Chapter 12 HERONâ€™S FORMULA
- Chapter 4 Equations In Two Variables
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 13 Volume and Surface Area
- chapter 14 Statistics
- Chapter 15 Probability
- Chapter 11: Constructions

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