Constructions: compass, ruler and protractor
Read a protractor without falling for the trap, bisect lines and angles, construct 60°, 30°, 90° and 45°, and build a triangle from three sides. Read one step, play with it, then tap “I understand this”.
The tools and the protractor
For constructions you need a sharp pencil, a ruler (straight lines and lengths), a compass (arcs and circles) and a protractor (measuring angles). Never rub out your construction arcs: they are your proof.
- Put the centre of the protractor exactly on the vertex.
- Lay the 0 line on one arm of the angle.
- Start at that 0 and count up to the other arm. Read on the same scale.
The protractor
Turn the arm left or right and change the angle. Watch which scale you read.
Every number on a protractor has a partner: 50 and 130 are in the same place. Ask yourself: is the angle acute (smaller than 90°) or obtuse (bigger than 90°)?
Bisect a line: the perpendicular bisector
To bisect a line means to cut it into two equal parts. With a compass you get the middle and a 90° angle, without measuring.
Construct the perpendicular bisector
Tap “Next step”. The red part is what you draw now.
P and Q are the same distance from A and from B (the same compass width). All points that are the same distance from A and B lie on one straight line, and that line goes exactly through the middle of AB, at 90°.
Bisect an angle
To bisect an angle, you cut it into two equal angles. You use the compass again, and the compass width stays the same for the two arcs inside the angle.
Construct the bisector
Tap “Next step”.
Angles without a protractor: 60°, 30°, 90° and 45°
- 60°: two arcs with the same compass width make an equilateral triangle.
- 30°: bisect the 60°.
- 90°: construct a perpendicular at a point on the line.
- 45°: bisect the 90°.
Construct the angle
Choose 60° · 30° or 90° · 45° and tap through the steps.
OP, OQ and PQ are all three the same length (one compass width). That is an equilateral triangle, and its three angles are equal: 180° ÷ 3 = 60°.
Construct a triangle from three sides
If you know all three sides, you draw one side with the ruler and find the third corner with two compass arcs.
Triangle ABC
Tap “Next step”.
Does it not work? The two shorter sides together must be longer than the longest side. With 2 cm, 3 cm and 8 cm the arcs will never cross.
Play: protractor and constructions
Read and think
Read the protractor or think about the construction, and choose the answer.
Correct: 0Check yourself
- Protractor: centre on the vertex, 0 line on one arm, and read the scale that starts at that 0.
- Perpendicular bisector: arcs from A and B with the same width (more than half), join the crossing points.
- 60° with two equal arcs; bisect for 30°. 90° with a perpendicular; bisect for 45°.
- Triangle from three sides: draw one side, find the third corner with two compass arcs. Do not rub out the arcs.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 4 A4 pagesPractice sheet
- Geometry8 pages · PDFPaperMemo
- Space and shape10 pages · PDFPaperMemo
Ready for more? The Grade 7 constructions quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Do one construction together on paper, with a real compass. Then look at the steps here to check if you did it right.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.