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Pack A — Fluency

Ecolint Campus des NationsMathematics
Year 8 · 8.16 Constructions

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Describe how to measure an angle using a protractor.
     
  2. 2.
    A protractor reading is 130°. Identify whether the angle is acute, right, obtuse, or reflex.
     
  3. 3.
    Construct an angle of 60° using a compass on a starting line. Describe the steps.
     
  4. 4.
    Describe how to copy a given line segment using a compass and straight-edge.
     
  5. 5.
    A right angle is what number of degrees? Describe how to construct a perpendicular through a point on a line.
     
  6. 6.
    Construct an equilateral triangle on a given segment AB using compass and straightedge. Describe the construction.
     
  7. 7.
    Sketch and describe how to bisect a line segment AB using compass and ruler.
     
  8. 8.
    The "seed of life" is a classical construction. Describe it.
     
  9. 9.
    Sketch the inscribed regular hexagon in a circle. Why does the construction work?
     
  10. 10.
    Use compass and ruler to construct a 30° angle. Describe.
     
SilverQuestions 11–20
  1. 11.
    Construct a triangle with sides 5 cm, 6 cm, 7 cm using compass and ruler.
     
  2. 12.
    Bisect an angle of 80°. Describe the steps and find the resulting angle.
     
  3. 13.
    Construct a 45° angle.
     
  4. 14.
    Construct a triangle with sides 6 cm, 6 cm, 6 cm. What type of triangle is this?
     
  5. 15.
    Construct a regular hexagon inscribed in a circle of radius 4 cm.
     
  6. 16.
    A perpendicular bisector of segment AB passes through the midpoint and is at 90° to AB. Why is every point on this bisector equidistant from A and B?
     
  7. 17.
    Construct a square of side 5 cm.
     
  8. 18.
    Construct a 15° angle. Describe.
     
  9. 19.
    Why can a 60° angle be constructed but not a 20° angle with compass and straightedge only?
     
  10. 20.
    A construction involves "marking and arc". Describe the difference between drawing an arc and a full circle.
     
GoldQuestions 21–30
  1. 21.
    Construct an isosceles triangle with base 6 cm and equal sides 5 cm each. Calculate the height from apex to base.
     
  2. 22.
    A right-angled triangle has legs 3 and 4. Construct it and verify the hypotenuse using Pythagoras.
     
  3. 23.
    Construct the perpendicular bisector of a 10 cm segment. Verify that midpoint is 5 cm from each endpoint and the bisector is at 90°.
     
  4. 24.
    Construct a regular pentagon inscribed in a circle. (Outline the steps for the standard ruler-and-compass construction.)
     
  5. 25.
    A 75° angle can be constructed as 60° + 15° (or 45° + 30°). Describe both methods.
     
  6. 26.
    Construct the seed-of-life flower (7 interlocking circles). Describe the procedure and the angles created at the centres.
     
  7. 27.
    A regular hexagon has side 8 cm. Find (a) the radius of the inscribed circle (apothem) and (b) the radius of the circumscribed circle.
     
  8. 28.
    Construct a parallel to a given line through an external point. Describe.
     
  9. 29.
    Construct a triangle with sides 5, 5, 5 cm. Find the area without measuring (use Pythagoras to find the height).
     
  10. 30.
    A protractor reading of 47° is given. Construct (without protractor!) an angle of 47° approximately — list approximate methods and their limits.
     
PlatinumQuestions 31–40
  1. 31.
    Construct an equilateral triangle on a given segment AB, then construct its **circumscribed circle** (passing through all three vertices).
     
  2. 32.
    Describe how to construct a regular pentagon with side 5 cm using only ruler and compass.
     
  3. 33.
    Verify the "seed of life" structure: six surrounding circles in a hexagonal pattern. Why is this geometric arrangement special?
     
  4. 34.
    Construct a triangle with sides 7 cm, 8 cm, 9 cm. Calculate its area using Heron's formula.
     
  5. 35.
    A complex construction: starting from an equilateral triangle ABC, construct the perpendicular from one vertex to the opposite side. What is the relationship between this perpendicular and the median?
     
  6. 36.
    Trisect a 90° angle — is this possible using only compass and straightedge?
     
  7. 37.
    Construct a regular hexagon with apothem 4 cm. Find the side length.
     
  8. 38.
    Construct a triangle similar to a given triangle with sides 3, 4, 5 cm, but with a linear scale factor of 1.5.
     
  9. 39.
    Construct an inscribed regular dodecagon (12-gon) in a circle. Outline the procedure.
     
  10. 40.
    In a circle of radius 5 cm, construct an isosceles trapezium with parallel sides 6 cm and 8 cm.