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# Constructions Tutorials

Welcome to the construction zone!

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 using mathematical principles and tools. These tools used are the following:

– Usual **essentials**: Pencil, Rubber, Ruler, Sharpener etc.

– **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. Swipe the slider along the bottom to follow along!

## Basic Constructions

If you’re starting from scratch or having trouble with more advanced constructions, 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: