Study MaterialsCBSE NotesLines and Angles Class 7 Notes Maths Chapter 5

Lines and Angles Class 7 Notes Maths Chapter 5

 

CBSE Class 7 Maths Notes Chapter 5 Lines and Angles

A line segment has two endpoints and it is denoted by \(\bar { AB }\).
Lines and Angles Class 7 Notes Maths Chapter 5 1

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    A ray has only one end point (its initial point) and it is denoted by \(\vec { AB }\).
    Lines and Angles Class 7 Notes Maths Chapter 5 2

    A line has no end points on either side and it is denoted by \(\overleftrightarrow { AB }\).
    Lines and Angles Class 7 Notes Maths Chapter 5 3

    If a single straight line passes through three or more points, the points are said to be collinear.
    Lines and Angles Class 7 Notes Maths Chapter 5 4
    A, B, C are collinear points.

    An angle is formed when two lines (or rays or line – segments) meet.
    Lines and Angles Class 7 Notes Maths Chapter 5 5

    If the sum of measures of two angles is 90°, they are called complementary angles.
    e.g. ∠A = 60°, ∠B = 30°
    ∠A + ∠B = 60° + 30° = 90°

    If the sum of measures of two angles is 180°, they are called supplementary angles.
    e.g. ∠A = 150°, ∠B = 30°
    ∠A + ∠B = 150° + 30° = 180°

    If two angles have a common vertex and a common arm but no common interior, they are said to adjacent angles.
    Lines and Angles Class 7 Notes Maths Chapter 5 6

    If two angles are adjacent and supplementary, they are said to be linear pair.
    Lines and Angles Class 7 Notes Maths Chapter 5 7
    x + y = 180°.

    When two lines meet at some point, they are said to be intersecting lines. The meeting point is called the point of intersection.
    Lines and Angles Class 7 Notes Maths Chapter 5 8

    When two lines drawn on a sheet of paper do not meet, however far produced, they are said to be parallel lines.
    Lines and Angles Class 7 Notes Maths Chapter 5 9

    When two lines intersect, then the pair of opposite angles is said to vertically opposite angles. They are equal in measure.
    A transversal line intersects two or more lines at distinct points.
    Lines and Angles Class 7 Notes Maths Chapter 5 10

    A transversal line gives rise to several types of angles.

    Types of Angles Angles
    Interior Angles ∠3, ∠4, ∠5, ∠6
    Exterior Angles ∠1, ∠2, ∠7, ∠8
    Corresponding Angles ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8
    Alternate Interior Angles ∠3 and ∠6, ∠4 and ∠5
    Alternate Exterior Angles ∠1 and ∠8, ∠2 and ∠7
    The interior on the same side of the transversal ∠3 and ∠5, ∠4 and ∠6

    When a transversal cuts two parallel lines, then
    Lines and Angles Class 7 Notes Maths Chapter 5 11
    (a) Corresponding angles are equal.
    ∠1 = ∠5, ∠3 = ∠7, ∠2 = ∠6, ∠4 = ∠8
    (b) Alternate interior angles are equal.
    ∠3 = ∠6, ∠4 = ∠5
    (c) Interior angles on the same side of transversal are supplementary.
    ∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°.

    When the measure of the angle is less than 90°, it is said to be an acute angle.

    When the measure of the angle is equal to 90°, it is said to the right angle.

    When the measure of the angle is greater than 90°, it is said to the obtuse angle.

    When the measure of the angle is greater than 180°, it is said to be the reflex angle.

    A line segment has two endpoints.

    A ray has only one endpoint (its vertex).

    A line has no endpoints on either side.

    An angle is formed when two lines (or rays or line-segments) meet.

    Complementary Angles
    When the sum of the measures of two angles is 90°, the angles are called complementary angles.

    Supplementary Angles
    When the sum of the measures of two angles is 180°, the angles are called supplementary angles.

    Adjacent Angles
    A pair of angles which are placed next to each other in such a way that they have a common vertex and an arm which is common to both the angles are called adjacent angles.

    Linear Pair
    A linear pair is a pair of adjacent angles whose non-common arms are opposite rays.
    A pair of angles placed adjacent to each other is called a linear pair if the sum of their measures is 180°.
    Note: A pair of supplementary angles form a linear pair when placed adjacent to each other.

    When two lines intersect, the vertically opposite angles so formed are equal.
    Lines and Angles Class 7 Notes Maths Chapter 5 12
    ∠1 + ∠2 = 180° …(1)
    ∵ ∠1 and ∠2 form a linear pair
    ∠3 + ∠2 = 180° …(2)
    ∵ ∠3 and ∠2 form a linear pair
    From (1) and (2)
    ∠1 = ∠3
    Similarly, we can prove that ∠2 = ∠4

    Intersecting Lines
    Two lines intersect if they have a point in common called their point of intersection.

    Transversal
    A line that intersects two or more lines at different points is called a transversal.

    Transversal of Parallel Lines
    Lines and Angles Class 7 Notes Maths Chapter 5 13
    The lines on a plane that do not meet anywhere are called parallel lines.
    Transversal of parallel lines give rise to quite interesting results.

    We hope the given CBSE Class 7 Maths Notes Chapter 5 Lines and Angles Pdf free download will help you. If you have any query regarding NCERT Class 7 Maths Notes Chapter 5 Lines and Angles, drop a comment below and we will get back to you at the earliest.

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