CBSE Class 10 Mathematics (Standard) Chapter 6 Triangles Important Questions 2027
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25 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 3.6 questions per paper (OR alternatives counted separately)
- 3 question patterns repeated across papers
Important topics in Triangles
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Similarity criteria (AA, SSS, SAS) based problems | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Applied problems on similar triangles | Board 2024Board 2025Board 2026Sample 2025 | ★★☆☆☆ |
| 3 | Proof of BPT (theorem proof question) | Board 2023Board 2024Board 2026Sample 2026 | ★☆☆☆☆ |
| 4 | Basic Proportionality Theorem (Thales) and its converse | Board 2023Board 2026Sample 2025 | ★☆☆☆☆ |
Repeated questions from Triangles
1. Prove the Basic Proportionality Theorem
4×Board 2023Board 2024Board 2026Sample 20265 marks
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
2. Medians of similar triangles are proportional
2×Sample 2025Sample 20262 marks
If AP and DQ are medians of triangles ABC and DEF respectively, where triangle ABC ~ triangle DEF, then prove that AB/DE = AP/DQ
3. Compute length/perimeter via corresponding side ratios
2×Board 2026Sample 20261/2 marks
In the given figure, triangle AHK ~ triangle ABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find the length of AC.
Triangles questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 2 | 7 |
| Board 2024 | 3 | 12 |
| Board 2025 | 5 | 15 |
| Sample 2025 | 7 | 13 |
| Board 2026 | 5 | 15 |
| Sample 2026 | 3 | 8 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Triangles
Board 2026 5 questions
In triangles ABC and PQR, angle A = angle Q and angle B = angle R, then AB : AC is equal to : (A) PQ : PR (B) PQ : QR (C) QR : QP (D) PR : QR
In the given figure, triangle AHK ~ triangle ABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find the length of AC.
In the given figure, XY || QR, PQ/XQ = 7/3 and PR = 6.3 cm. Find the length of YR.
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Sample 2026 3 questions
If triangle ABC ~ triangle DEF, AB = 6cm, DE = 9cm, EF = 6cm and FD = 12cm, then the perimeter of triangle ABC is (A) 28cm (B) 28.5cm (C) 18cm (D) 23cm
If AP and DQ are medians of triangles ABC and DEF respectively, where triangle ABC ~ triangle DEF, then prove that AB/DE = AP/DQ
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Hence in triangle PQR, prove that a line l intersects the sides PQ and PR of a triangle PQR at L and M respectively such that LM || QR. If PL = 5.7cm, PQ = 15.2cm and MR = 5.5cm, then find the length of PM (in cm)
Board 2025 5 questions
In triangles ABC and DEF, angle B = angle E, angle F = angle C and AB = 3 DE. Then, the two triangles are : (A) congruent but not similar (B) congruent as well as similar (C) neither congruent nor similar (D) similar but not congruent
If triangle ABC ~ triangle PQR in which AB = 6 cm, BC = 4 cm, AC = 8 cm and PR = 6 cm, then find the length of (PQ + QR).
In the given figure, QR/QS = QT/PR and angle 1 = angle 2. Show that triangle PQS ~ triangle TQR. [figure: triangle TQR with P on QT and S on QR, angles 1 at Q and 2 at R marked]
The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that DF x EF = FB x FA.
In triangle ABC, if AD is perpendicular to BC and AD2 = BD x DC, then prove that angle BAC = 90 deg.
Sample 2025 7 questions
O is the point of intersection of two chords AB and CD of a circle. If angle BOC = 80 deg and OA = OD then triangle ODA and triangle OBC are A) equilateral and similar B) isosceles and similar C) isosceles but not similar D) not similar
[case context] A triangular cabinet design: largest triangle ABC, smallest triangle DEF with shelf PQ parallel to EF. (i) Show that triangle DPQ ~ triangle DEF.
[case context] Triangular cabinet, triangle DEF with PQ parallel to EF. (ii) If DP = 50 cm and PE = 70 cm then find PQ/EF.
[case context] Triangular cabinet with triangles ABC and DEF. (iii)(A) If 2AB = 5DE and triangle ABC ~ triangle DEF then show that (perimeter of triangle ABC)/(perimeter of triangle DEF) is constant.
[case context] Triangular cabinet with similar triangles ABC and DEF. (iii)(B) If AM and DN are medians of triangles ABC and DEF respectively then prove that triangle ABM ~ triangle DEN.
In triangle ABC, D, E and F are midpoints of BC, CA and AB respectively. Prove that triangle FBD ~ triangle DEF and triangle DEF ~ triangle ABC.
In triangle ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ.
Board 2024 3 questions
In the given figure, ABCD is a quadrilateral. Diagonal BD bisects angle B and angle D both. Prove that: (i) triangle ABD ~ triangle CBD (ii) AB = BC
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.
In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that 1/x + 1/z = 1/y
Board 2023 2 questions
In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY. [Figure: triangle ABC with line XZ parallel to BC, X on AB, Z on AC, Y on cevian AM]
If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, prove that the other two sides are divided in the same ratio.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 6 Triangles?
By how often and how recently they were asked: Similarity criteria (AA, SSS, SAS) based problems; Applied problems on similar triangles; Proof of BPT (theorem proof question).
How many marks does Triangles carry in the CBSE Class 10 Mathematics (Standard) exam?
Triangles is part of the Geometry unit, which carries 15 marks in the official syllabus. In the analysed papers it had about 3.6 questions per paper.
Do questions from Triangles repeat in board exams?
Yes — 3 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.