Constructing a triangle given three side lengths using compasses
I can construct a triangle given the three required side lengths.
- Year 11
Constructing a triangle given three side lengths using compasses
I can construct a triangle given the three required side lengths.
Lesson details
Key learning points
- The first side can be drawn accurately with a ruler
- A pair of compasses should be used to indicate potential positions for the other sides, by drawing arcs
- Where the two remaining sides intersect is where the two sides should be drawn to
- All triangles with the same measurements are congruent
Keywords
Pair of compasses - A pair of compasses is a tool which can be used to draw circles and arcs. A pair of compasses is sometimes referred to just as a compass.
Radius - The radius is any line segment that joins the centre of a circle to any point on its circumference.
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Arc - An arc is part of a curve. An arc of a circle is part of the circle’s circumference.
Common misconception
Pupils may try to draw the triangle using only a pencil and ruler, rather than construct it using a pair of compasses.
Remind pupils that if the task is to 'construct' then they must use their geometry equipment.
Equipment
Pair of compasses, ruler, protractor.
Licence
Prior knowledge starter quiz
6 Questions
Q1.Supplementary angles are a pair of angles that sum to °.
Q2.The diagram shows the perpendicular bisector of AB that passes through the point P. The perpendicular intersects AB at point O. Which of these constructions will produce a 45° angle?

Q3.EC is a perpendicular to AD. The angle AOC is bisected. Match each angle to its size.

Angle AOB - 45°
Angle BOD - 135°
Angle COD - 90°
Reflex angle BOD - 225°
Reflex angle BOC - 315°
Q4.The line segments AB and BC form an angle of 120°. Which of these constructions creates a 60° angle?

Q5.Line segments AB and BC are the legs of a 136° angle. The diagram shows the two constructions that are applied to ABC. The angle $$x$$° is °.

Q6.Line segments AB and BC are the legs of a 136° angle. The diagram shows the two constructions that are applied to ABC. The angle $$z$$° is °.

Assessment exit quiz
6 Questions
Q1.Jacob sets his compasses to the width shown in the diagram. Without changing the setting, Jacob draws a circle. The diameter of the circle is cm.

Q2.What equipment do you need in order to accurately construct a triangle given the length of 3 sides?
Q3.Jun is using GeoGebra to accurately draw a triangle with side lengths 6 units, 8 units and 10 units. Which of these tools should Jun use to draw the first side of the triangle?

Q4.Jun and Izzy both accurately construct triangles of sides 6 cm, 7 cm and 9 cm. Which statement is correct?

Q5.Here are two circles with centres A and B. The circles meet at C and D. The radius of the circles are 7.2 cm and 9.1 cm. The distance between their centres is 6.4 cm. Match each length to its value.

AB - 6.4 cm
CA - 7.2 cm
BD - 9.1 cm