Knowledge organisers

Triangles – Congruence Theorems: CBSE Class 9 Maths knowledge organiser

Everything to know about triangles – congruence theorems 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

Congruent triangles: Triangles with all three sides and all three angles equal, so one fits exactly on the other.
SAS: Two sides and the angle between them are equal, so the triangles are congruent.
CPCT: Corresponding parts of congruent triangles are equal.

Key formulas

Congruence: SSS, SAS, ASA/AAS, RHS (not SSA, not AAA); then CPCT. \(\triangle ABC\cong\triangle PQR\): \(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\)
Isosceles: equal sides ⇔ equal opposite angles; median to the base ⟂ base and bisects the vertex angle
"If \(P\) then \(Q\)": converse "if \(Q\) then \(P\)"; one counterexample disproves

Worked example

\(\triangle ABC \cong \triangle LMN\) with \(\angle A = 40^\circ\) and \(\angle B = 75^\circ\). Find \(\angle N\).

\(N\) corresponds to \(C\): \(\angle N = \angle C = 180^\circ - 40^\circ - 75^\circ = 65^\circ\).

Common mistakes

Using SSA (or AAA) as a congruence condition.
Writing the congruence in the wrong order, so CPCT pairs the wrong sides.
Using SAS when the angle is not between the two sides.
Assuming a converse is true because the original statement is true.

You should be able to…

Match the parts of congruent triangles, name the congruence rules and write converses and counterexamples.
Prove short results with SAS, SSS, ASA, AAS and RHS and use the isosceles-triangle theorems.
Write complete congruence proofs and explain why a triangle is rigid.
Explain why SSA fails, test several converses at once and repair a false converse.

The printable sheet

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