CBSE Class 10 Mathematics: Triangles — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: State and prove the Basic Proportionality Theorem (Thales' theorem).
  Ans: Statement: If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. Given: △ABC, DE ∥ BC. To prove: AD/DB = AE/EC. Proof: Draw DM ⊥ AE and EN ⊥ AD. Area(△ADE)/Area(△DBE) = (½ × AE × DM)/(½ × AE × EN) ... Using equal areas of triangles with same base DE: Area(△DBE) = Area(△DEC) (between parallel lines DE and BC). Therefore AD/DB = AE/EC.
• Q: The sides of two similar triangles are in ratio 4:9. Find the ratio of their areas.
  Ans: Ratio of areas of similar triangles = (ratio of corresponding sides)² = (4/9)² = 16/81. If sides are 4:9, areas are 16:81.
• Q: In △ABC, AD is the bisector of ∠A. If AB = 6 cm, AC = 8 cm, BD = 3 cm, find DC.
  Ans: By Angle Bisector Theorem: BD/DC = AB/AC. 3/DC = 6/8. DC = 3 × 8/6 = 4 cm.

Exam Tips for This Chapter

• Revise all definitions and laws from Triangles — they are commonly asked as 1-2 mark questions
• Practice diagrams related to Triangles — neat labelled diagrams carry 2-3 marks
• For numericals, always show formula → substitution → answer with correct units
• Previous year analysis shows Triangles carries 8-12 marks in the board exam