Class 10 Maths Triangles Worksheet — Free Printable PDF
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⭐ MeritMate — Class 10 Maths: Triangles
Curriculum-Aware · meritmate.in# Triangles
Class 10 Mathematics Worksheet
Name: _________________ Date: _________________ Roll No: _________________
Section A: Multiple Choice Questions
*(1 mark each)*
Q1. If △ABC ~ △PQR and the ratio of their corresponding sides is 3:5, then the ratio of their areas is:
a) 3:5
b) 9:25
c) 6:10
d) 27:125
Q2. In △DEF, a line XY is drawn parallel to EF such that DX:XE = 2:3. What is the ratio of the area of △DXY to the area of trapezium XYFE?
a) 4:25
b) 4:21
c) 2:3
d) 9:25
Q3. In the given figure, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, then BD is equal to:
a) 22/3 cm
b) 55/3 cm
c) 64/3 cm
d) 55/8 cm
Q4. A vertical pole of height 6 m casts a shadow 4 m long on the ground. At the same time, a tower casts a shadow 28 m long. The height of the tower is:
a) 48 m
b) 42 m
c) 56 m
d) 36 m
Q5. Which of the following conditions is NOT sufficient to prove that two triangles are similar?
a) AAA (Angle-Angle-Angle)
b) SAS (Side-Angle-Side)
c) SSS (Side-Side-Side)
d) ASS (Angle-Side-Side)
Section B: Fill in the Blanks
*(1 mark each)*
Q6. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and the two triangles are said to be similar by the ________ criterion.
Q7. The line drawn parallel to one side of a triangle divides the other two sides proportionally. This theorem is known as the ________.
Q8. In △ABC, if DE ∥ BC, AD = 4 cm, DB = 6 cm and AE = 3 cm, then EC = ________.
Q9. If △ABC ~ △QRP, ar(△ABC)/ar(△QRP) = 9/4, AB = 18 cm and BC = 15 cm, then the length of PR is ________.
Q10. Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are ________.
Section C: Short Answer Questions
*(2 marks each)*
Q11. State and prove the Basic Proportionality Theorem (BPT).
Q12. In the figure, △OAB ~ △OCD. If AB = 6 cm, CD = 4 cm, OA = 3 cm and OD = 2 cm, find OB and OC.
Q13. The diagonals of a trapezium ABCD, where AB ∥ DC, intersect each other at point O. Show that:
$$\frac{OA}{OC} = \frac{OB}{OD}$$
Q14. In a △ABC, D and E are points on AB and AC respectively such that DE ∥ BC. If AD = 2.4 cm, AE = 3.2 cm and EC = 4.8 cm, find AB.
Q15. Prove that if the areas of two similar triangles are equal, then the triangles are congruent.
⭐ Answer Key
Class 10 · Maths · Triangles# Answer Key
Section A: Multiple Choice Questions
| Q. No | Answer | Explanation |
|--------|--------|-------------|
| Q1 | (b) 9:25 | Ratio of areas of similar triangles = (ratio of corresponding sides)² = 3²:5² = 9:25 |
| Q2 | (b) 4:21 | DX:XE = 2:3, so DE:DX = 5:2 → ar(△DXY)/ar(△DEF) = 4/25. ar(trapezium) = 25−4 = 21 units → ratio = 4:21 |
| Q3 | (b) 55/3 cm | ∠ACB = ∠CDA → △ACB ~ △ADC (AA). So AC/AD = AB/AC → AB = AC²/AD = 64/3. BD = AB − AD = 64/3 − 3 = 55/3 cm |
| Q4 | (b) 42 m | Using similar triangles: Height/Shadow = 6/4. Tower height = (6/4) × 28 = 42 m |
| Q5 | (d) ASS (Angle-Side-Side) | ASS is not a valid similarity or congruence criterion as it does not uniquely determine triangle similarity |
Section B: Fill in the Blanks
| Q. No | Answer |
|--------|--------|
| Q6 | AA (Angle-Angle) or AAA similarity criterion |
| Q7 | Basic Proportionality Theorem (BPT) or Thales' Theorem |
| Q8 | EC = 4.5 cm *(By BPT: AD/DB = AE/EC → 4/6 = 3/EC → EC = 18/4 = 4.5 cm)* |
| Q9 | PR = 10 cm *(ar ratio = 9/4, so side ratio = 3/2 → BC/PR = 3/2 → PR = 15×2/3 = 10 cm)* |
| Q10
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