Triangles

What you'll learn

Master similar triangles, the Basic Proportionality Theorem, and the criteria (AA, SSS, SAS) that power Class 10 geometry proofs and problems.

This chapter has

Triangles — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   Two figures having the same shape but not necessarily the same size are called:

   • Acongruent
   • Bsimilar
   • Cequal
   • Dproportional
   Show answer & solution

   Correct answer: (B) similar

   Similar figures have the same shape (equal angles, proportional sides) but may differ in size.

2. Q2medium

   The Basic Proportionality Theorem (BPT) states that if a line is drawn parallel to one side of a triangle, it divides the other two sides:

   • Aproportionally
   • Bequally
   • Cat right angles
   • Dinto equal halves
   Show answer & solution

   Correct answer: (A) proportionally

   BPT (Thales' theorem): DE ∥ BC in △ABC → AD/DB = AE/EC.

3. Q3easy

   Two triangles are similar if their corresponding angles are equal. This criterion is called:

   • ASSS
   • BAA
   • CSAS
   • DRHS
   Show answer & solution

   Correct answer: (B) AA

   AA (Angle-Angle) similarity criterion — if two angles of one triangle equal two angles of another, they are similar.

4. Q4medium

   In △ABC and △DEF, if AB/DE = BC/EF = CA/FD, the triangles are similar by:

   • AAA
   • BSAS
   • CSSS
   • DRHS
   Show answer & solution

   Correct answer: (C) SSS

   All three corresponding sides are proportional → SSS similarity criterion.

5. Q5medium

   In △ABC, if DE ∥ BC with D on AB and E on AC, and AD/DB = 2/3, then AE/EC = ?

   • A2/3
   • B3/2
   • C2/5
   • D3/5
   Show answer & solution

   Correct answer: (A) 2/3

   By BPT, AE/EC = AD/DB = 2/3.

6. Q6easy

   Pythagoras' theorem states that in a right-angled triangle:

   • Aa + b = c
   • Ba² + b² = c²
   • Ca² = b² + c²
   • Da + b = c²
   Show answer & solution

   Correct answer: (B) a² + b² = c²

   Hypotenuse² = Sum of squares of the other two sides: c² = a² + b².

7. Q7easy

   In a right-angled triangle, the sides are 3, 4 and 5 units. Which is the hypotenuse?

   • A3
   • B4
   • C5
   • Dall equal
   Show answer & solution

   Correct answer: (C) 5

   3² + 4² = 9 + 16 = 25 = 5². So 5 is the hypotenuse (opposite the right angle).

8. Q8hard

   If △ABC ~ △PQR, then the ratio of their areas equals:

   • AAB/PQ
   • B(AB/PQ)²
   • CAB²/PQ
   • D√(AB/PQ)
   Show answer & solution

   Correct answer: (B) (AB/PQ)²

   The ratio of areas of similar triangles = square of the ratio of corresponding sides.

Want the full set? Practise all 15 Triangles questions →