A line is a straight, endless path extending in both directions. It is defined by two points and has only length .

An angle is formed when two rays diverge from a common point called the vertex. Angles are measured in degrees .

What is a ray and a line segment?

A ray starts from one point and extends infinitely in one direction, whereas a line segment connects two points and has a definite length .

Define collinear and non-collinear points.

Collinear points lie on the same line; non-collinear points do not lie on the same line .

List types of angles with their definitions.

Acute (0°–90°), Right (90°), Obtuse (90°–180°), Straight (180°), Reflex (180°–360°), Complete (360°) .

What are complementary and supplementary angles?

Complementary angles sum to 90°, supplementary angles sum to 180° .

What are adjacent, vertically opposite, and linear pair angles?

Adjacent: Share a common arm and vertex; Vertically opposite: Formed when two lines intersect, equal in measure; Linear pair: Two adjacent angles whose non-common arms form a line (sum = 180°) .

State the angle sum property of a triangle.

The sum of the angles in any triangle is \(180^\circ\) .

State the angle sum property for polygons.

The sum of interior angles of an n-sided polygon is \((n-2) \times 180^\circ(n-2)\)

What is a transversal?

A transversal is a line that intersects two or more lines at distinct points .

Name angles formed when a transversal cuts two parallel lines.

Corresponding, Alternate Interior, Alternate Exterior, Co-interior (Consecutive Interior) angles .

State properties of parallel lines with a transversal.

Corresponding angles are equal; Alternate interior angles are equal; Co-interior angles are supplementary .

What is the linear pair axiom?

The sum of the angles forming a linear pair is \(180^\circ\)

State vertically opposite angles theorem.

Vertically opposite angles formed by intersecting lines are equal .

Give a real-life application of lines and angles.

Used in engineering, architectural design, navigation, and geographical surveys .

NCERT Class 9 Maths Chapter 6 Lines and Angles

8 CBSE Marks

★★★★★ Difficulty

9 Topics

High Board Weight

Topics Covered

9 key topics in this chapter

Basic Terms & Definitions

Pairs of Angles: Complementary & Supplementary

Adjacent & Vertically Opposite Angles

Linear Pair Axiom

Parallel Lines & Transversal

Corresponding Angles Axiom

Alternate Interior Angles Theorem

Co-interior Angles

Angle Sum in a Triangle

Study Resources

📖 NCERT Notes ✏️ MCQ Practice 🏆 CBSE PYQs 📝 Exercise Solutions ✅ True / False Quiz

Key Formulas & Identities

Formula / Rule	Expression
Supplementary	\(∠A + ∠B = 180°\)
Complementary	\(∠A + ∠B = 90°\)
Vertically Opposite	\(∠1 = ∠3, ∠2 = ∠4\)
Corresponding (∥ lines)	\(∠1 = ∠5 (\text{F-shape})\)
Alternate Interior	\(∠3 = ∠5 (\text{Z-shape)}\)
Co-interior	\(∠3 + ∠6 = 180° (\text{C-shape)}\)
Triangle Angle Sum	\(∠A + ∠B + ∠C = 180°\)
Exterior Angle	\(∠ext = ∠A + ∠B (\text{remote interior)}\)

Important Points to Remember

Vertically opposite angles are equal. Adjacent angles on a straight line sum to 180° (Linear Pair Axiom).

Corresponding angles axiom: if a transversal crosses two parallel lines, corresponding angles are equal, and conversely.

Alternate interior angles are equal when lines are parallel. Co-interior (same-side interior) angles are supplementary (sum = 180°).

Angle sum in a triangle = 180°. Exterior angle of a triangle = sum of the two non-adjacent interior angles.

Lines and Angles

Topics Covered

Study Resources

Key Formulas & Identities

Important Points to Remember

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