Ruler and compass constructions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Constructing with a ruler and compasses

Mathematics · Geometry · ages 12-14
Name ______________________   Date ____________

  1. You need a protractor to construct an angle bisector accurately.

    Circle one:   True   False

  2. An angle of 80° is bisected with compasses and a straight edge. What does each half measure?

    • 20°
    • 40°
    • 80°
    • 160°

  3. A segment is 10 cm long. Its perpendicular bisector crosses it. How far is the crossing point from each end in centimetres?

    Answer: ______________

  4. Which construction uses a ruler and compasses to drop a straight line down to meet another line at a right angle from an outside point?

    • Perpendicular from a point to a line
    • Angle bisector
    • Perpendicular bisector of a segment

  5. Which fact is true of every point on the perpendicular bisector of segment AB?

    • It is twice as far from A as from B
    • It sits on the segment AB itself
    • It is 10 cm from the midpoint
    • It is the same distance from A as from B

  6. Farid needs a perpendicular from point P down to line AB, using only a ruler and compasses. What should he draw first?

    • A straight line from P straight down by eye
    • An arc centered on a point already on line AB
    • An arc centered on P that crosses line AB in two places

  7. A 124° angle is bisected and each half is measured to check the construction. What should each half read in degrees?

    Answer: ______________

  8. To construct a perpendicular bisector, you draw an arc above and below the line from point A, then an arc above and below the line from point B, all with the same compass width. How many arcs do you draw in total?

    Answer: ______________

  9. Lucia bisects angle ABC. Her first arc from B crosses the two arms at X and Y. She then draws an arc from X, but changes the compass width before drawing an arc from Y. Is the line through where those two arcs cross the true bisector?

    • Yes, because only the first arc from B needs to be accurate
    • No, the arcs from X and Y must use the same width, or they won't cross at the true bisector point
    • Yes, because both arcs still crossed somewhere

  10. An equilateral triangle with side 8 cm is built using compasses and a straight edge. What is its perimeter in centimetres?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Constructing with a ruler and compasses W1-mt_ZrsqGVG-Wt-s1

  1. False · Compass arcs find the exact halfway line. No protractor is needed.
  2. 40° · Bisecting halves the angle: 80 / 2 = 40°.
  3. 5 · The bisector halves the segment: 10 / 2 = 5 cm from each end.
  4. Perpendicular from a point to a line · This construction is called a perpendicular from a point to a line. It meets the line at exactly 90 degrees.
  5. It is the same distance from A as from B · The bisector is the set of points equidistant from both ends.
  6. An arc centered on P that crosses line AB in two places · The first arc, centered on P, marks two points on AB. Those two points set up the rest of the construction.
  7. 62 · Half of 124° is 62°, and both halves matching confirms the bisection.
  8. 4 · Two arcs from A and two arcs from B make four arcs. The two crossing points give you the bisector line.
  9. No, the arcs from X and Y must use the same width, or they won't cross at the true bisector point · The arcs centered on X and Y must match in width. Different widths can still cross, but not at the exact halfway point.
  10. 24 · All three sides are 8 cm, so the perimeter is 3 x 8 = 24 cm.
Worksheet · LightMySky