Triangles
Similarity, BPT, areas of similar triangles, Pythagoras applications.
In the official syllabus: Unified Council — National Science Talent Search Examination - Syllabus (Classes 1 to 10), Class 9 paper, Mathematics section; also Class 10 paper, Mathematics section (syllabus page 2) (read 29 Sept 2026).
Test yourself on Triangles
Practice questions for NSTSE on this topic with instant answers — no signup.
2 practice questions on Triangles for NSTSE, with answers
Shishya's practice questions, written with AI. Each answer was checked by an automated second pass, not by a person.
1.In △ABC, DE is parallel to BC, with D on AB and E on AC. If AD = 4 cm, DB = 6 cm, and AE = 3 cm, then EC equals:
- (A)4.5 cm
- (B)5 cm
- (C)6 cm
- (D)4 cm
Show the answer and solution
Answer: (A) 4.5 cm
Solution: By Basic Proportionality Theorem: AD/DB = AE/EC, so 4/6 = 3/EC. Cross-multiplying: 4×EC = 18, hence EC = 4.5 cm.
2.In triangle ABC, D is a point on BC such that BD = 3 cm and DC = 5 cm. If the area of triangle ABD is 18 cm², what is the area of triangle ABC?
- (A)30 cm²
- (B)40 cm²
- (C)48 cm²
- (D)54 cm²
Show the answer and solution
Answer: (C) 48 cm²
Solution: Triangles ABD and ABC share the same height from A. Their areas are in the ratio of their bases BD:BC = 3:8. So area of ABC = 18 × (8/3) = 48 cm².
Study notes are still being prepared.
Don't wait — Shishya can teach you this topic right now, on demand.
Ask Shishya to teach this →Need more? Ask Shishya
Shishya is your personal tutor for this topic. Pick a starter or open a free chat.
- Go deeper on this topicGo deeper on Triangles for NSTSE — examples and edge cases I should know.
- Show me exam shortcutsGive me 3 fastest shortcuts to solve Triangles questions in the exam.
- What mistakes should I avoid?What are the most common mistakes students make on Triangles? How do I avoid them?
- Quiz me adaptivelyQuiz me on Triangles — start with one easy question, then go harder based on how I answer.