Basic Proportionality Theorem
- CBSE · NCERT Class 10, Ch 6 Triangles
The Basic Proportionality Theorem says that when a line runs parallel to one side of a triangle, it splits the other two sides in equal ratios.
It is also called the Thales Theorem. In ∆ABC, let DE be parallel to BC, with D on AB and E on AC. Then AD/DB = AE/EC. The converse is also true: a line that cuts two sides of a triangle in equal ratios must run parallel to the third side.
A small example
In ∆ABC, DE ∥ BC. AD = 3 cm, DB = 6 cm and AE = 2 cm. Find EC.
- By the theorem, AD/DB = AE/EC.
- So 3/6 = 2/EC, which gives EC = 4 cm.
Where marks go
The proof of this theorem is a 5-mark question in both 2026-27 CBSE sample papers. In the Maths Basic marking scheme for 2026-27 (Question 32), the figure, given, to prove and construction earn half a mark each. That is 2 marks in all. The proof itself earns the other 3.
In the Maths Standard marking scheme (Question 33), those four parts together earn 1 mark and the proof 2 marks. The last 2 marks are for using the theorem on a trapezium. So a correct proof with no labelled figure or construction gives up the marks the scheme sets aside for them. Our note on step marking explains this split.
Sources
Facts last checked against these sources on 30 September 2026.
- Mathematics, Class X (2026-27), Chapter 6: Triangles · NCERT
- Mathematics Basic (241) Marking Scheme, Class X 2026-27 - Question 32 · CBSE Academic Unit
- Mathematics Standard (041) Marking Scheme, Class X 2026-27 - Question 33 · CBSE Academic Unit
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