Chapter 13: Practical Geometry - Mock Test
Instructions
- •This test covers all constructions and concepts from Chapter 13
- •Questions are arranged as per CBSE paper pattern
- •Section A: 6 questions × 1 mark = 6 marks (MCQ/Fill blanks)
- •Section B: 8 questions × 2 marks = 16 marks (Short constructions)
- •Section C: 6 questions × 3 marks = 18 marks (Long constructions)
- •Show all construction lines and arcs clearly
- •For constructions, accuracy within 1-2 mm is acceptable
- •No negative marking
Mock Test Questions
Section A: 1 Mark Questions (6 × 1 = 6 marks)
1. What is the perpendicular bisector of a line segment?
Show Answer
Answer: A line that divides the segment into two equal parts and meets it at 90°
2. Which triangle construction criterion uses all three sides?
Show Answer
Answer: SSS (Side-Side-Side)
3. What compass width should be used for perpendicular bisector of segment AB?
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Answer: More than half of AB
4. Write scale 1:100 in words. 1 cm = ? m
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Answer: 1 cm = 1 m (or 100 cm)
5. Is SSA (side-side-angle) a valid triangle construction criterion?
Show Answer
Answer: No, SSA is not a valid criterion. It can give two different triangles.
6. Name the criterion used when two angles and included side are given.
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Answer: ASA (Angle-Side-Angle)
Section B: 2 Mark Questions - Short Constructions (8 × 2 = 16 marks)
7. Construct the perpendicular bisector of line segment AB = 7 cm.
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Answer: Draw AB = 7 cm. Open compass to >3.5 cm. From A, draw arcs above and below. From B, with same width, draw arcs intersecting at P and Q. Join PQ. This is the perpendicular bisector.
8. Construct a perpendicular to line AB at point P on the line.
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Answer: Mark equal distances on both sides of P on AB, at C and D. From C and D, draw equal arcs intersecting at Q. Join PQ perpendicular to AB.
9. Bisect angle ABC = 50° using compass and straightedge.
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Answer: From B, draw arc cutting BA at P and BC at Q. From P and Q, draw equal arcs intersecting at R. Join BR. BR bisects the angle into two 25° angles.
10. Copy angle PQR = 60° to a new location using compass.
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Answer: Draw arc from Q cutting QP and QR at P' and R'. Draw ray from X. From X draw arc of same radius. Set compass to P'R' distance, mark on new arc. Join to form angle equal to 60°.
11. Construct triangle ABC with sides AB = 5 cm, BC = 6 cm, AC = 5 cm.
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Answer: Draw AB = 5 cm. From A, open compass to 5 cm, draw arc. From B, open to 6 cm, draw arc intersecting at C. Join AC and BC. Triangle complete (SSS).
12. Construct triangle with AB = 4 cm, angle A = 45°, AC = 5 cm (SAS).
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Answer: Draw AB = 4 cm. At A, construct 45° angle. On second arm, mark AC = 5 cm. Join BC. Triangle complete (SAS).
13. A plot is 60 m long. Draw it to scale 1:200. What is drawing length?
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Answer: Scale 1:200 means 1 cm = 200 cm = 2 m. Drawing length = 60 m ÷ 2 = 30 cm. Draw line of 30 cm.
14. On a map with scale 1:50,000, two cities are 3 cm apart. Find actual distance.
Show Answer
Answer: Actual distance = 3 cm × 50,000 = 150,000 cm = 1500 m = 1.5 km
Section C: 3 Mark Questions - Complex Constructions (6 × 3 = 18 marks)
15. Construct triangle PQR with angles P = 50°, Q = 60°, and side PQ = 6 cm (ASA).
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Answer: Step 1: Draw base PQ = 6 cm Step 2: At P, construct 50° angle using protractor or angle bisector method Step 3: At Q, construct 60° angle Step 4: Extend rays from P and Q until they meet at R Step 5: Triangle PQR is complete (ASA criterion)
16. Construct right triangle ABC with hypotenuse AC = 8 cm, angle B = 90°, and AB = 5 cm (RHS).
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Answer: Step 1: Draw hypotenuse AC = 8 cm Step 2: Find midpoint O of AC using perpendicular bisector Step 3: From O, draw semicircle with radius 4 cm Step 4: From A, open compass to 5 cm and draw arc intersecting semicircle at B Step 5: Join AB and BC - angle ABC = 90° with required measurements
17. A rectangular field is 150 m by 100 m. Draw to scale 1:1000. Calculate area in cm².
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Answer: Scale 1:1000: 1 cm = 1000 cm = 10 m Length in drawing: 150 m ÷ 10 = 15 cm Width in drawing: 100 m ÷ 10 = 10 cm Draw rectangle 15 cm × 10 cm Area in drawing = 15 × 10 = 150 cm²
18. Construct triangle PQR with PQ = 7 cm, angle Q = 55°, angle R = 65°.
Show Answer
Answer: Step 1: Find angle P = 180° - 55° - 65° = 60° Step 2: Draw base PQ = 7 cm (included side for ASA) Step 3: At P, construct 60° angle Step 4: At Q, construct 55° angle Step 5: Extend rays to meet at R - triangle PQR complete
19. On a map scale 1:2,00,000, distance between two cities is 2.5 cm. What is actual distance in km?
Show Answer
Answer: Scale 1:2,00,000 means 1 cm = 2,00,000 cm Actual distance = 2.5 × 2,00,000 = 5,00,000 cm = 5,000 m = 5 km
20. Construct triangle ABC with sides AB = 6 cm, BC = 8 cm, AC = 10 cm. Then construct perpendicular bisector of AB.
Show Answer
Answer: Triangle construction (SSS): Step 1: Draw AB = 6 cm (base) Step 2: From A, open compass to 10 cm, draw arc Step 3: From B, open compass to 8 cm, draw arc intersecting at C Step 4: Join AC and BC - triangle complete Perpendicular bisector of AB: Step 5: Open compass to >3 cm from A, draw arcs above and below AB Step 6: From B with same width, draw arcs intersecting at P and Q Step 7: Join PQ - this is perpendicular bisector of AB
Marking Scheme & Evaluation
Section A (1 Mark)
1 mark for correct answer. No partial marking.
Section B (2 Marks)
- • Correct construction with all lines and arcs: 2 marks
- • Correct method but minor inaccuracy (>2mm error): 1 mark
- • Incomplete or incorrect construction: 0 marks
Section C (3 Marks)
- • Correct construction with proper steps and accuracy: 3 marks
- • Correct method, minor construction errors: 2 marks
- • Partial construction showing understanding: 1 mark
- • No attempt or completely wrong: 0 marks
Performance Analysis
36-40 marks: Excellent! You have mastered practical geometry constructions.
30-35 marks: Very Good! Strong understanding of construction techniques and methods.
24-29 marks: Good! Practice more on accuracy and showing construction lines.
18-23 marks: Average. Focus on understanding each construction step.
Below 18 marks: Need improvement. Review construction methods step-by-step.
Exam Preparation Tips
- ✓Always show construction lines and arcs clearly - marks are given for method
- ✓Keep compass fixed at same width for related construction steps
- ✓For triangle constructions, identify given information first (SSS/SAS/ASA/RHS)
- ✓Use sharp pencil and light lines initially, darken important constructions
- ✓Mark scale and all important points clearly on your drawing
- ✓For scale problems, always identify scale denominator and apply correctly