Knowledge organisers

4-gons (Quadrilaterals): CBSE Class 9 Maths knowledge organiser

Everything to know about 4-gons (quadrilaterals) 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

Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Mid-point theorem: The segment joining the mid-points of two sides of a triangle is parallel to the third side and half its length.
Diagonal: A line segment joining two opposite vertices.

Key formulas

Parallelogram: opposite sides/angles equal, diagonals bisect; rhombus diagonals ⟂; rectangle diagonals equal
Mid-point theorem	\(DE\parallel BC,\) \(DE=\tfrac12BC\)
Centroid divides each median 2 : 1	\(AG=\tfrac23AD,\) \(G=\left(\tfrac{x_1+x_2+x_3}3,\ \tfrac{y_1+y_2+y_3}3\right)\)
Joining mid-points of any quadrilateral gives a parallelogram, perimeter \(AC+BD\), half the area

Worked example

In parallelogram \(PQRS\), \(\angle P = (3x + 10)^\circ\) and \(\angle Q = (2x + 20)^\circ\). Find \(x\).

Adjacent angles: \(5x + 30 = 180 \Rightarrow x = 30\); \(\angle P = 100^\circ\), \(\angle Q = 80^\circ\).

Common mistakes

Taking adjacent angles of a parallelogram as equal: they are supplementary.
Assuming the diagonals of every parallelogram are equal or perpendicular.
Using the ratio \(1 : 2\) for the centroid from the vertex: it is \(2 : 1\).
Using the mid-point theorem when only one point is a mid-point: use the converse, with the parallel line.

You should be able to…

Use the angle and side properties of parallelograms, the mid-point theorem and the centroid ratio.
Find unknown sides and angles and prove short results about parallelograms and mid-points.
Prove the mid-point theorem and work with the mid-point quadrilateral in coordinates and in words.
Use the converse of the mid-point theorem in trapeziums and classify mid-point quadrilaterals.

The printable sheet

4-gons (Quadrilaterals) knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — 4-gons (Quadrilaterals) 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 · Lines and Angles · Triangles – Congruence Theorems · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers