Basic Proportionality Theorem: Class 10 practice
If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio: AD/DB = AE/EC.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Ratio and proportion
The idea behind basic proportionality theorem
If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio: AD/DB = AE/EC.
Step-by-step method
- Check the line is parallel to a side.
- Write AD/DB = AE/EC.
- Cross-multiply and solve.
Worked example 1 (Basic)
In △ABC, DE ∥ BC with AD = 2 cm, DB = 3 cm and AE = 4 cm. Find EC.
- AD/DB = AE/EC
- EC = 4 × 3 ÷ 2 = 6 cm
- Answer: 6 cm
Worked example 2 (Standard)
In △ABC, DE ∥ BC with AD = 7 cm, DB = 6 cm and AE = 14 cm. Find EC.
- AD/DB = AE/EC
- EC = 14 × 6 ÷ 7 = 12 cm
- Answer: 12 cm
Worked example 3 (Challenge)
In △ABC, DE ∥ BC with AD = x cm, DB = 4 cm, AE = (x + 3) cm and EC = 7 cm. Find x.
- x/4 = (x + 3)/7
- 7x = 4x + 12
- x = 4
- Answer: x = 4 cm
Common mistakes and misconceptions
- Using AD/AB with DB/EC
- Applying it when the line isn't parallel
Practice questions
- (Basic) In △ABC, DE ∥ BC with AD = 7 cm, DB = 5 cm and AE = 17.5 cm. Find EC.
- (Basic) In △ABC, DE ∥ BC with AD = 2 cm, DB = 9 cm and AE = 3 cm. Find EC.
- (Standard) In △ABC, DE ∥ BC with AD = 3 cm, DB = 9 cm and AE = 6 cm. Find EC.
- (Standard) In △ABC, DE ∥ BC with AD = 3 cm, DB = 6 cm and AE = 7.5 cm. Find EC.
- (Challenge) In △ABC, DE ∥ BC with AD = x cm, DB = 4 cm, AE = (x + 6) cm and EC = 6 cm. Find x.
- (Challenge) In △ABC, DE ∥ BC with AD = x cm, DB = 3 cm, AE = (x + 8) cm and EC = 5 cm. Find x.
Answer key with full working
- Q1: AD/DB = AE/EC → EC = 17.5 × 5 ÷ 7 = 12.5 cm → Answer: 12.5 cm
- Q2: AD/DB = AE/EC → EC = 3 × 9 ÷ 2 = 13.5 cm → Answer: 13.5 cm
- Q3: AD/DB = AE/EC → EC = 6 × 9 ÷ 3 = 18 cm → Answer: 18 cm
- Q4: AD/DB = AE/EC → EC = 7.5 × 6 ÷ 3 = 15 cm → Answer: 15 cm
- Q5: x/4 = (x + 6)/6 → 6x = 4x + 24 → x = 12 → Answer: x = 12 cm
- Q6: x/3 = (x + 8)/5 → 5x = 3x + 24 → x = 12 → Answer: x = 12 cm
Syllabus note
This skill is listed under "Triangles" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is basic proportionality theorem in?
"Triangles", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.