Knowledge organisers

Lines and Angles: CBSE Class 9 Maths knowledge organiser

Everything to know about lines and angles on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Complementary angles: Two angles that add up to 90°.
Supplementary angles: Two angles that add up to 180°.
Transversal: A line that crosses two or more lines; with parallel lines it makes equal corresponding and alternate angles.

Key formulas

Linear pair sums to 180°; vertically opposite angles are equal; reflex angle of \(\theta\) is \(360^\circ-\theta\)
Parallel lines: corresponding and alternate angles equal, co-interior angles sum to 180° (and conversely); \(l\parallel m,\ m\parallel n\Rightarrow l\parallel n\)
Angle sum 180°; exterior angle = sum of the two interior opposite angles; at least two angles of a triangle are acute

Worked example

Lines \(AB\) and \(CD\) meet at \(O\), and \(\angle AOC = 48^\circ\). Find \(\angle BOD\), \(\angle AOD\) and \(\angle BOC\).

\(\angle BOD = 48^\circ\) (vertically opposite); \(\angle AOD = 180^\circ - 48^\circ = 132^\circ\) (linear pair); \(\angle BOC = 132^\circ\) (vertically opposite).

Common mistakes

Calling co-interior angles equal: they are supplementary.
Using parallel-line facts when the lines are not given as parallel.
Taking the reflex angle of \(\theta\) as \(180^\circ + \theta\) instead of \(360^\circ - \theta\).
Writing angle facts without the reason in brackets.

You should be able to…

Classify angles and use linear pairs, vertically opposite angles and parallel-line angle facts.
Find unknown angles with reasons and prove the basic theorems on intersecting lines.
Write complete proofs with parallel lines and the angles of a triangle.
Argue by contradiction about the angles of a triangle and solve multi-step angle problems.

The printable sheet

Lines and Angles knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Lines and Angles knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers