Knowledge organisers

Triangles: CBSE Class 10 Maths knowledge organiser

Everything to know about triangles 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

Similar figures: Same shape but not necessarily the same size: equal angles and sides in the same ratio.
Basic Proportionality Theorem: A line parallel to one side of a triangle divides the other two sides in the same ratio.
Criteria for similarity: AA, SSS and SAS similarity show two triangles are similar.

Key formulas

Basic Proportionality Theorem: if \(DE\parallel BC\) in \(\triangle ABC\)	\(\frac{AD}{DB}=\frac{AE}{EC}\)
Converse: if a line divides two sides in the same ratio, it is parallel to the third side
Similar triangles (AA, SSS, SAS): corresponding angles equal, corresponding sides in the same ratio
Pythagoras (right angle at \(B\))	\(AC^2=AB^2+BC^2\)

Worked example

\(DE \parallel BC\), \(AD = 5\), \(DB = 3\), \(AC = 12\). Then \(\dfrac{AE}{AC} = \dfrac{AD}{AB} = \dfrac58 \Rightarrow AE = 7.5\).

Common mistakes

Writing \(\dfrac{AD}{DB} = \dfrac{DE}{BC}\) — wrong; use \(\dfrac{AD}{AB} = \dfrac{DE}{BC}\).
Matching vertices in the wrong order, leading to wrong side ratios.
Using SAS similarity with an angle that is not between the two sides.
Claiming two rhombuses/rectangles are similar from sides alone.

You should be able to…

You know when figures are similar and can use the Basic Proportionality Theorem to find missing lengths.
Prove triangles similar using AA, SAS or SSS with a reason for every step, and use the converse of BPT.
Write the BPT proof and the long 'prove that' answers the board asks, with figure, given, to prove, construction and proof.
Handle the hard proofs: altitudes, parallelograms with extended sides, and algebraic BPT problems.

The printable sheet

Triangles knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Triangles knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers