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The chapter Lines and Angles provides the first introduction to geometrical fundamentals. The chapter investigates basic geometric elements that start with points and lines, and rays and continues to explain angle varieties produced by transversal intersections or cuts of lines. Basic geometric understanding depends on these core concepts for learning advanced mathematical shapes that appear later in the textbook.
The chapter covers four angle types - acute, right, obtuse, and straight - combined with complementary, supplementary, adjacent and vertically opposite angle pairs. The study of lines intersecting with transversals results in the evaluation of corresponding angles and alternate interior angles, along with other angle properties. All advanced geometry studies require a fundamental understanding of these concepts. Students should utilise the NCERT class 9th maths notes to learn and review various concepts, while using the NCERT notes for supplementary notes on higher-level chapters if needed.
A portion of the line with two endpoints is called a line segment. It is denoted by the symbol $\overline{AB}$.
A part of the line with one endpoint and the other endpoint extending up to infinity. It is denoted by the symbol $\overrightarrow{AB}$.
If three or more points lie on the same line, they are called collinear points.
If three or more points do not lie on the same line, they are called non-collinear points.
An angle is generated when two rays originate from the same point. The rays making an angle are called the arms of the angle, while the vertex refers to the place where they end.
In geometry, there are several types of angles. The fundamental component of geometry in Mathematics is the angles.
When the sum of two angles is 90°, they form up complementary angle.
When the sum of two angles is 180°, they form up supplementary angle.
If angles have a common vertex, a common arm, and their non-common arms are on different sides of the common arm, they are called adjacent angles.
A pair of adjacent angles whose non-common sides create a straight line that adds up to 180°.
If two lines intersect each other at a point, they form vertically opposite angles which are equal to each other. Like in the given figure, angles a and c, b and d are vertically opposite angles.
When the lines cross each other at a single point, they are called Intersecting lines.
When the lines are parallel to each other, or do not intersect, they are called non-intersecting lines.
If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.
If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.
If two lines intersect each other, then the vertically opposite angles are equal.
A transversal defines a line which crosses different lines at different points. Like in the figure, t is the transversal line.
When a transversal intersects two parallel lines, then the Corresponding Angles are Equal.
When a transversal line intersects two lines and the Corresponding Angles are equal, then the lines are parallel to each other.
When a transversal intersects two parallel lines, then the pair of alternate interior angles is equal.
When a transversal line intersects two lines and the alternate interior angles are equal, then the lines are parallel to each other.
When a transversal intersects two parallel lines, then the pair of interior angles on the same side of the transversal line are supplementary, i.e. equal to 180°.
When a transversal line intersects two lines and the interior angles on the same side of the transversal line are supplementary, then the lines are parallel to each other.
Students must download the notes below for each chapter to ace the topics.
Students must check the NCERT solutions for Class 10 Maths and Science given below:
Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:
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