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Gyaan Maths
CBSE · Class 6-10
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CBSE Maths · Class 6

Chapter 14: Practical Geometry

Name: ________________________
Date: ______________
Marks: ____ / 10

Constructions using ruler and compass — circles, line segments, angles, perpendicular bisectors.

Questions

  1. List instruments in a geometry box.
  2. Angle constructed by bisecting 60∘60^\circ.
  3. To construct a 75∘75^\circ angle, use which combination?
  4. How would you draw a 75∘75^\circ angle using compass?
  5. Construct perpendicular bisector — how many arcs?
  6. Angle bisector divides an angle into?
  7. Which instruments are used in constructions?
  8. Can you construct 40∘40^\circ using only ruler and compass?
  9. Construct a copy of ∠PQR\angle PQR: what's the first arc drawn?
  10. Angle that can be trisected with ruler and compass?

Extra Practice (Optional)

  • Construct 105∘105^\circ.
  • Construct a perpendicular to a line at a given external point.
  • Draw a triangle with sides 5,6,75, 6, 7.

Answer Key (For Teachers)

  1. Answer: 55 instruments.
    Working: Ruler, compass, protractor, set squares, divider.
  2. Answer: 30∘30^\circ.
    Working: 60/260/2.
  3. Answer: 60∘+12(30∘)60^\circ + \tfrac{1}{2}(30^\circ).
    Working: 60∘+15∘60^\circ + 15^\circ; 15∘=15^\circ = half of 30∘30^\circ.
  4. Answer: As described.
    Working: Bisect 90∘90^\circ and 60∘60^\circ to get 75∘75^\circ (average of the two).
  5. Answer: 22
    Working: Two — one from each endpoint of the segment.
  6. Answer: Two equal halves.
    Working: Two equal parts.
  7. Answer: Ruler + compass.
    Working: No markings on ruler; compass for arcs.
  8. Answer: No (needs protractor).
    Working: It's known to be non-constructible in general (needs protractor).
  9. Answer: Arc at QQ.
    Working: Arc at vertex QQ cutting both arms.
  10. Answer: Straight (180∘180^\circ).
    Working: Straight angle can be trisected into 60∘60^\circ.
Gyaan Maths · CBSE Class 6 · Chapter 14
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026