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Constructions Tutorials
One of the tricky elements of geometry is the “construction” – a task whereby students must use their tools to construct up to 22 geometric shapes and figures.
You will need:
– Compass: Used for drawing circles and arcs.
– Protractor: Used for measuring and drawing angles.
– Set Square / “Triangle” : Typically 45-degree and 60-degree triangles used for drawing perpendicular lines.
Here’s how to complete all 22 of the construction tasks, step by step.
Basic Constructions
If you’re starting from scratch, this is the place to start.
Using only a compass and straight edge, bisect the angle shown:
Using only a compass and a straightedge, construct a perpendicular bisector on the line shown:
Construct a line perpendicular to the current line, passing through the point A.
Construct a line perpendicular to the current line, passing through the point A.
Construct a line perpendicular to the current line, passing through the point A.
Line Segment Constructions
Construct a line perpendicular to the current line, passing through the point A.
Construct a line segment of 6cm on the given ray |AB|:
Angle Constructions
Construct an angle of 60° with the given ray below:
Construct an angle of 60° without using a protractor or set square, but a compass and a straight edge only. Show all work clearly:
Triangle Constructions
Construct a triangle with sides 4cm, 5cm, and 6cm:
Construct a Right Angle Triangle ABC where |AB| = 6cm, |∠BAC| = 70° and |AC| = 4cm. Show your construction lines clearly:
Construct a Right Angle Triangle ABC where |AB| = 6cm, |∠BAC| = 70° and |∠ABC| = 30°. Show your construction lines clearly:
Construct a Right Angle Triangle ABC where the hypotenuse |BC| = 10cm, and |AB| = 6cm. Show your construction lines clearly:
Construct a Right Angle Triangle ABC where |AB| = 5cm, and |∠ACB| = 60°. Show your construction lines clearly:
Rectangle and Parallelogram Constructions
Construct a Rectangle ABCD where |AB| = 12cm and |AC| = 4cm. Show your construction lines clearly:
Construct a Parallelogram ABCD where |AB| = 8cm, |AC| = 5cm, and |∠BAC| = 60°. Show your construction lines clearly:
Circle Constructions
Construct the circumcentre and circumcircle of the Triangle XYZ shown below, using only a compass and a straight edge. Label the circumcentre C. Show your construction lines clearly:
Construct the incentre and incircle of the Triangle XYZ shown below, using only a compass and a straight edge. Label the incircle. Show your construction lines clearly:
Construct the line tangent to the circle with centre C at point T using only a Compass and Straight Edge. Show all workings clearly:
Construct the line tangent to the circle with centre C at point T using only a Compass and Straight Edge. Show all workings clearly:
Construct the orthocentre of the Triangle XYZ shown below, using only a compass and a straight edge. Label the orthocentre. Show your construction lines clearly:
