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Class 10 Triangles: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 6, Triangles, each with a worked answer. They cover what the chapter asks: finding a missing side of similar triangles, using the basic proportionality theorem and its converse, and deciding whether two triangles are similar by AA, SSS or SAS. Try each one on paper before you open the answer. Another Class 10 geometry set, on tangents to a circle, is Class 10 Circles.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Six facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 6, printed pages 73 to 98) cover every question below:
- Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio (section 6.3, page 79).
- Basic proportionality theorem (Theorem 6.1): if a line is drawn parallel to one side of a triangle to meet the other two sides in distinct points, it divides those two sides in the same ratio (page 80).
- Converse (Theorem 6.2): if a line divides two sides of a triangle in the same ratio, the line is parallel to the third side (page 82).
- AAA criterion (Theorem 6.3): if the corresponding angles of two triangles are equal, the triangles are similar (page 87); the summary adds the AA criterion, that two equal angles are enough (page 97).
- SSS criterion (Theorem 6.4): if the sides of one triangle are proportional to the sides of another, the triangles are similar (page 88).
- SAS criterion (Theorem 6.5): if one angle of a triangle equals one angle of another and the sides including them are proportional, the triangles are similar (page 90).
Similar triangles and missing sides
Question 1. Triangles ABC and PQR are similar, with AB = 4 cm, PQ = 6 cm and BC = 8 cm. Find QR in cm.
Answer: Corresponding sides are in the same ratio: QR/BC = PQ/AB = 6/4. So QR = 8 × 6/4 = 12 cm.
Question 2. A 6 m pole has a 4 m shadow. A tower nearby has a 28 m shadow at that moment. How tall is the tower, in m?
Answer: The sun makes similar triangles with the pole and with the tower, so height ÷ shadow is the same: 6 ÷ 4 = h ÷ 28, and h = 6 × 28 ÷ 4 = 42 m.
The basic proportionality theorem and its converse
Question 3. In triangle ABC, DE ∥ BC, with AD = 3 cm, DB = 6 cm and AE = 2 cm. Find EC in cm.
Answer: By the basic proportionality theorem, AD/DB = AE/EC: 3/6 = 2/EC, so EC = 2 × 6 ÷ 3 = 4 cm.
Question 4. In triangle ABC, D is on AB and E is on AC, with AD = 4 cm, DB = 6 cm and AE = 6 cm. How long must EC be, in cm, for DE to be parallel to BC?
Answer: By the converse, DE ∥ BC when AD/DB = AE/EC: 4/6 = 6/EC, so EC = 6 × 6 ÷ 4 = 9 cm.
Question 5. In triangle ABC, DE ∥ BC with AD = 2 cm, AB = 6 cm and BC = 9 cm. Find DE in cm.
Answer: Triangle ADE is similar to triangle ABC (the parallel line makes equal corresponding angles), so DE ÷ BC = AD ÷ AB = 2 ÷ 6. DE = 9 × 2 ÷ 6 = 3 cm.
Which criterion proves similarity?
Question 6. In triangles ABC and DEF, ∠A = ∠D = 50° and ∠B = ∠E = 60°. Are the triangles similar? Which criterion do you use?
Answer: yes, by the AA criterion. Two angles of one triangle equal two angles of the other. (The third angles are also equal: ∠C = 180° − 50° − 60° = 70° and ∠F = 70°, so this is the AAA situation too.)
Question 7. The sides of triangle ABC are 3 cm, 4 cm and 5 cm. The sides of triangle DEF are 6 cm, 8 cm and 10 cm. Are the triangles similar? Which criterion do you use?
Answer: yes, by the SSS criterion. Compare the sides in order: 3/6 = 1/2, 4/8 = 1/2 and 5/10 = 1/2. All three ratios are equal, so the triangles are similar.
Question 8. In triangles ABC and PQR, ∠A = ∠P = 40°, AB = 4 cm, AC = 6 cm, PQ = 6 cm and PR = 9 cm. Are the triangles similar? Which criterion do you use?
Answer: yes, by the SAS criterion. The equal angles are ∠A and ∠P, and the sides including them are proportional: AB/PQ = 4/6 = 2/3 and AC/PR = 6/9 = 2/3. So triangle ABC is similar to triangle PQR.
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Triangles questions. Questions 1 to 5 above are all in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- See which unit this chapter belongs to and how CBSE splits the 80 theory marks in our Class 10 Maths syllabus 2026-27 guide.
- The same step-by-step style for neighbouring chapters: Class 10 Polynomials and Class 10 Pair of Linear Equations.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.
- NCERT, Mathematics, Textbook for Class X, Chapter 6 "Triangles" (Reprint 2026-27), printed pages 73-98 (similar triangles, section 6.3, page 79; Theorem 6.1, page 80; Theorem 6.2, page 82; the AAA criterion, Theorem 6.3, page 87; the SSS criterion, Theorem 6.4, page 88; the SAS criterion, Theorem 6.5, page 90; the AA criterion, summary, page 97): ncert.nic.in/textbook/pdf/jemh106.pdf
The theorems and criteria are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.