Measuring, Drawing and Constructing
Measuring, drawing and constructing covers using a ruler and protractor accurately to measure and draw lines and angles, and using compasses to construct triangles from given information (three sides, or two sides and the angle between them) and to construct a perpendicular bisector or an angle bisector. Accuracy matters: every construction line and compass arc should be left visible on the diagram as evidence of the method used.
Before you start
Make sure you're comfortable with these topics first:
Method
- To measure a line, line up the zero mark of the ruler exactly with one end of the line, then read the length at the other end.
- To measure an angle, place the centre of the protractor exactly on the vertex and the base line along one arm of the angle, then read off the correct scale, checking first whether the angle looks acute or obtuse.
- To construct a triangle given three sides (SSS), draw the longest side first, then use compasses set to the length of each other side to draw arcs from each end, and join the intersection point to both ends.
- To construct a triangle given two sides and the angle between them (SAS), draw one side, use a protractor to mark the given angle at one end, draw the second side along this angle, then join the two open ends.
- To construct a perpendicular bisector, set compasses to more than half the line length, draw arcs from both ends above and below the line, and join the two points where the arcs cross.
- Leave every construction arc visible on your diagram; a construction with no arcs showing may lose marks even if the final drawing looks correct.
Worked example
Construct triangle ABC with AB = 6 cm, angle A = 50 degrees, and AC = 8 cm. Describe each step.
- Draw line AB exactly 6 cm long using a ruler.
- Place a protractor at point A, with its base line along AB, and mark a point at 50 degrees.
- Draw a straight line from A through this mark, at least 8 cm long.
- Set compasses to 8 cm, and from A, mark point C on this new line.
- Join B to C with a straight line to complete the triangle.
Practice questions
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Q1What piece of equipment is used to measure the size of an angle?Show answer
Answer: A protractor
Q2What piece of equipment is used to construct an accurate triangle when you know the length of all three sides?Show answer
Answer: Compasses, together with a ruler
Q3A triangle has sides 5 cm, 5 cm and 8 cm. Which side should you draw first when constructing it, and why?Show answer
Answer: The 8 cm side, because it is easiest to draw the given, longest side first with a ruler, then use compasses to find the third vertex.
Q4When measuring an angle that looks obtuse, and the protractor shows both 40 and 140 at the same point, which reading should you use?Show answer
Answer: 140 degrees, since the angle is obtuse (between 90 and 180 degrees).
Q5Name the construction that finds all points equidistant from two given points.Show answer
Answer: The perpendicular bisector of the line joining the two points.
Q6What does SAS stand for in triangle construction?Show answer
Answer: Side, Angle, Side (two given sides with the given angle between them).
Q7Why must you leave your compass arcs visible when constructing a perpendicular bisector?Show answer
Answer: To show the method used and give evidence of an accurate construction; the arcs confirm the two arc centres were an equal distance apart.
Q8A line AB is 9 cm long. To construct its perpendicular bisector, to what minimum distance should you set your compasses?Show answer
Answer: More than 4.5 cm, which is more than half of AB.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Construct triangle DEF with DE = 7 cm, DF = 5 cm and EF = 6 cm, using compasses and a ruler. Leave in all construction arcs.
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(a) Construct the perpendicular bisector of a line segment PQ of length 8 cm. (b) Explain how your construction shows that every point on the perpendicular bisector is the same distance from P as it is from Q.
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Free printable worksheet
Want more practice on paper? Download the measuring, drawing and constructing worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 6 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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