CBSE Class 10 Mathematics (Basic) Chapter 6 Triangles Important Questions 2027
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27 questions from Triangles appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Geometry unit — 15 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 3.9 questions per paper (OR alternatives counted separately)
- 7 question patterns repeated across papers
Important topics in Triangles
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Similarity criteria (AA, SSS, SAS) based problems | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Proof of BPT (theorem proof question) | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| 3 | Applied problems on similar triangles | Board 2023Sample 2026 | ★☆☆☆☆ |
| 4 | Basic Proportionality Theorem (Thales) and its converse | Board 2023Sample 2026 | ★☆☆☆☆ |
Repeated questions from Triangles
1. Prove the Basic Proportionality Theorem
3×Board 2024Sample 2025Sample 20265 marks
Prove that a line drawn parallel to one side of a triangle intersecting other two sides in distinct points, divides the other two sides in the same ratio.
2. Perimeter/ratio of similar triangles
2×Board 2023Sample 20261 marks
If ΔABC ∼ ΔPQR (with AB = 3 cm, BC = 4 cm, AC = 5 cm and PR = 10 cm as shown), then perimeter of the triangle PQR (in cm) is
A) 12
B) 24
C) 18
D) 20
3. Which is NOT a similarity criterion
2×Board 2025Board 20261 marks
Which of the following is not the criterion for similarity of triangles ? (A) AAA (B) SSS (C) SAS (D) RHS
4. Angle P via SAS similarity from two figures
2×Board 2025Board 20261 marks
From the figures given below, which of the following is true about the measure of ∠ P ? [Triangle ABC with ∠B = 60°, ∠A = 80°, AB = 3.8 cm, AC = 3√3 cm, BC = 6 cm; Triangle PQR with PR = 6√3 cm, RQ = 7.6 cm, PQ = 12 cm] (A) ∠ P = 60° (B) ∠ P = 80° (C) ∠ P = 40° (D) The measure of ∠ P cannot be determined
5. Prove triangles similar from PQ || RS
2×Board 2025Board 20262 marks
In the given figure, if PQ ∥ RS, then prove that Δ POQ ~ Δ SOR.
6. Find unknown angles from a given similarity
2×Board 2025Board 20262 marks
In the given figure, Δ OSR ~ Δ OQP, ∠ ROQ = 125° and ∠ ORS = 70°. Find the measures of ∠ OSR and ∠ OQP.
7. State BPT and prove a trapezium
2×Board 2025Board 20265 marks
State “Basic Proportionality Theorem” and use it to prove the following : In a quadrilateral ABCD, diagonals AC and BD intersect each other at O such that AO/BO = CO/DO as shown in the given figure. Prove that ABCD is a trapezium.
Triangles questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 6 | 11 |
| Board 2024 | 3 | 12 |
| Board 2025 | 5 | 11 |
| Sample 2025 | 4 | 8 |
| Board 2026 | 5 | 11 |
| Sample 2026 | 4 | 8 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Triangles
Board 2026 5 questions
Which of the following is not the criterion for similarity of triangles ? (A) AAA (B) SSS (C) SAS (D) RHS
From the figures given below, which of the following is true about the measure of ∠ P ? [Triangle ABC with ∠B = 60°, ∠A = 80°, AB = 3.8 cm, AC = 3√3 cm, BC = 6 cm; Triangle PQR with PR = 6√3 cm, RQ = 7.6 cm, PQ = 12 cm] (A) ∠ P = 60° (B) ∠ P = 80° (C) ∠ P = 40° (D) The measure of ∠ P cannot be determined
In the given figure, if PQ ∥ RS, then prove that Δ POQ ~ Δ SOR.
In the given figure, Δ OSR ~ Δ OQP, ∠ ROQ = 125° and ∠ ORS = 70°. Find the measures of ∠ OSR and ∠ OQP.
State “Basic Proportionality Theorem” and use it to prove the following : In a quadrilateral ABCD, diagonals AC and BD intersect each other at O such that AO/BO = CO/DO as shown in the given figure. Prove that ABCD is a trapezium.
Sample 2026 4 questions
If in ΔABC and ΔDEF, AB/EF = AC/DE then they will be similar when
A) ∠A = ∠D
B) ∠A = ∠E
C) ∠C = ∠F
D) ∠B = ∠E
If ΔABC ∼ ΔPQR (with AB = 3 cm, BC = 4 cm, AC = 5 cm and PR = 10 cm as shown), then perimeter of the triangle PQR (in cm) is
A) 12
B) 24
C) 18
D) 20
ASSERTION (A): Line joining the midpoints of two sides of triangle is parallel to the third side.
REASON (R): If a line divides two sides of a triangle in the same ratio then it is parallel to the third side.
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Prove that a line drawn parallel to one side of a triangle intersecting other two sides in distinct points, divides the other two sides in the same ratio.
Board 2025 5 questions
Which of the following is not the criterion for similarity of triangles ? (A) AAA (B) SSS (C) SAS (D) RHS
From the figures given below, which of the following is true about the measure of ∠P ? (Triangle ABC: AB = 3.8 cm, angle A = 80°, AC = 3√3 cm, angle B = 60°, BC = 6 cm; Triangle PQR: PR = 6√3 cm, RQ = 7.6 cm, PQ = 12 cm.) (A) ∠P = 60° (B) ∠P = 80° (C) ∠P = 40° (D) The measure of ∠P cannot be determined
In the given figure, if PQ ∥ RS, then prove that ΔPOQ ~ ΔSOR.
In the given figure, ΔOSR ~ ΔOQP, ∠ROQ = 125° and ∠ORS = 70°. Find the measures of ∠OSR and ∠OQP.
State “Basic Proportionality Theorem” and use it to prove the following : In a quadrilateral ABCD, diagonals AC and BD intersect each other at O such that AO/BO = CO/DO as shown in the given figure. Prove that ABCD is a trapezium.
Sample 2025 4 questions
If △ABC ~ △PQR such that 3AB = 2PQ and BC = 10 cm, then length QR is equal to (A) 10 cm (B) 15 cm (C) 20/3 cm (D) 30 cm
In the given figure, △BAC is similar to (A) △AED (B) △EAD (C) △ACB (D) △BCA
In the given figure, if △OCA ~ △OBD then ∠OAC is equal to (A) 58° (B) 55° (C) 128° (D) 52°
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Board 2024 3 questions
D is a point on the side BC of ΔABC such that ∠ADC = ∠BAC. Show that AC2 = BC × DC.
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that other two sides are divided in the same ratio.
Sides AB and BC and median AD of a ΔABC are respectively proportional to sides PQ and PR and median PM of ΔPQR. Show that ΔABC ~ ΔPQR.
Board 2023 6 questions
The sides of two similar triangles are in the ratio 4 : 7. The ratio of their perimeters is : (a) 4 : 7 (b) 12 : 21 (c) 16 : 49 (d) 7 : 4
In the given figure, AB || CD. If AB = 5 cm, CD = 2 cm and OB = 3 cm, then the length of OC is : (a) 15/2 cm (b) 10/3 cm (c) 6/5 cm (d) 3/5 cm
In the above figure, the criterion of similarity by which ΔABC ~ ΔPQR is : (a) SSA (Side – Side – Angle) Similarity (b) ASA (Angle – Side – Angle) Similarity (c) SAS (Side – Angle – Side) Similarity (d) AA (Angle – Angle) Similarity
In the given figure, ABC and AMP are two right triangles, right angled at B and M, respectively. Prove that Δ ABC ~ Δ AMP.
In the given figure, DE || AC and DF || AE. Prove that BF/FE = BE/EC.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/OD. Show that quadrilateral ABCD is a trapezium.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 6 Triangles?
By how often and how recently they were asked: Similarity criteria (AA, SSS, SAS) based problems; Proof of BPT (theorem proof question); Applied problems on similar triangles.
How many marks does Triangles carry in the CBSE Class 10 Mathematics (Basic) exam?
Triangles is part of the Geometry unit, which carries 15 marks in the official syllabus. In the analysed papers it had about 3.9 questions per paper.
Do questions from Triangles repeat in board exams?
Yes — 7 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.