Chapter 10: Properties of Triangles - Mock Test
Instructions
- •This test has 20 questions covering all topics from Chapter 10
- •Questions are arranged as per CBSE paper pattern
- •Section A: 10 questions × 1 mark = 10 marks
- •Section B: 6 questions × 2 marks = 12 marks
- •Section C: 4 questions × 4.5 marks = 18 marks
- •No negative marking
- •Show all working for marks
Mock Test Questions
Section A: 1 Mark Questions (10 × 1 = 10 marks)
1. What is the sum of all angles in a triangle?
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Answer: 180°
2. In triangle ABC, ∠A = 60°, ∠B = 50°. Find ∠C.
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Answer: ∠C = 180° - 60° - 50° = 70°
3. What is an equilateral triangle?
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Answer: A triangle with all three sides equal and each angle = 60°
4. Define isosceles triangle.
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Answer: A triangle with two sides equal and two base angles equal
5. A right triangle has one angle of 35°. What is the other acute angle?
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Answer: 90° - 35° = 55° (acute angles are complementary)
6. Can sides 4, 5, 9 form a triangle? Why?
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Answer: No. Because 4 + 5 = 9, not greater than 9. Need a + b > c
7. What is a median of a triangle?
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Answer: A line from vertex to midpoint of opposite side
8. What is an altitude of a triangle?
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Answer: A perpendicular from vertex to opposite side
9. In triangle PQR, exterior angle at R is 100°. If ∠P = 45°, find ∠Q.
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Answer: ∠Q = 100° - 45° = 55° (exterior angle = sum of remote interior angles)
10. The point where all medians meet is called:
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Answer: Centroid
Section B: 2 Mark Questions (6 × 2 = 12 marks)
11. In triangle ABC, angles are in ratio 2:3:4. Find all three angles.
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Answer: Let angles be 2x, 3x, 4x 2x + 3x + 4x = 180° 9x = 180°, x = 20° Angles: 40°, 60°, 80°
12. In isosceles triangle ABC with AB = AC and ∠A = 60°, find ∠B and ∠C.
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Answer: ∠B = ∠C (base angles) 60° + ∠B + ∠C = 180° 60° + 2∠B = 180° ∠B = ∠C = 60° (This is equilateral triangle!)
13. Verify that sides 3, 4, 5 can form a triangle.
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Answer: Check all conditions: 3 + 4 = 7 > 5 ✓ 4 + 5 = 9 > 3 ✓ 5 + 3 = 8 > 4 ✓ Yes, valid triangle
14. What is the range of possible values for third side if two sides are 6 and 9?
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Answer: By triangle inequality: |9 - 6| < x < 9 + 6 3 < x < 15
15. In triangle XYZ, exterior angle at Z is 130°. If ∠Y = 55°, find ∠X.
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Answer: Exterior angle = ∠X + ∠Y 130° = ∠X + 55° ∠X = 130° - 55° = 75°
16. An isosceles triangle has base angles of 55° each. Classify it by type of angles.
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Answer: Vertex angle = 180° - 55° - 55° = 70° All angles < 90° Therefore, it's an ACUTE triangle
Section C: 4.5 Mark Questions (4 × 4.5 = 18 marks)
17. In triangle ABC, angle B is twice angle A and angle C is 80°. Find all angles and classify by sides.
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Answer: Let ∠A = x, then ∠B = 2x ∠A + ∠B + ∠C = 180° x + 2x + 80° = 180° 3x = 100° x = 33.33° ∠A ≈ 33°, ∠B ≈ 67°, ∠C = 80° All angles different, so SCALENE triangle.
18. An isosceles right triangle has two equal sides. Find all angles and explain.
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Answer: In right triangle, one angle = 90° In isosceles, two angles are equal Since one angle is 90°, the other two must be: (180° - 90°)/2 = 45° each Angles: 90°, 45°, 45° This is a special right triangle called 45-45-90 triangle.
19. In triangle PQR, exterior angle at Q is 115° and ∠P = 50°. Find ∠R and verify using angle sum.
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Answer: Exterior angle at Q = ∠P + ∠R 115° = 50° + ∠R ∠R = 65° Interior ∠Q = 180° - 115° = 65° (linear pair) Verify: ∠P + ∠Q + ∠R = 50° + 65° + 65° = 180° ✓
20. A triangle has sides in ratio 3:5:7. Check if valid triangle. Find range for each side if perimeter is 30.
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Answer: Let sides be 3x, 5x, 7x Check inequality: 3x + 5x = 8x > 7x ✓ 5x + 7x = 12x > 3x ✓ 7x + 3x = 10x > 5x ✓ Valid triangle! Perimeter: 3x + 5x + 7x = 30 15x = 30 x = 2 Sides: 6, 10, 14 Verify: 6 + 10 = 16 > 14 ✓
Marking Scheme & Evaluation
Section A (1 Mark)
1 mark for correct answer. No partial marking.
Section B (2 Marks)
- • Correct answer with working: 2 marks
- • Correct method but minor error: 1 mark
- • No working shown: 0 marks
Section C (4.5 Marks)
- • Complete solution with verification: 4.5 marks
- • Correct approach with minor errors: 3 marks
- • Partially correct (≥50%): 2 marks
- • Relevant working shown: 1 mark
Performance Analysis
36-40 marks: Excellent! Master of triangle properties.
28-35 marks: Very Good! Strong understanding.
20-27 marks: Good! Review weaker concepts.
12-19 marks: Average. Practice more problems.
Below 12 marks: Needs improvement. Review fundamentals.
Exam Preparation Tips
- ✓Always verify angle sum = 180° in your final answer
- ✓For triangle inequality, check ALL three conditions
- ✓Exterior angle = sum of two REMOTE interior angles (not all three)
- ✓In isosceles triangle, clearly identify which angles are equal
- ✓Draw diagrams for visualization in complex problems