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Broad Topics > 2D Geometry, Shape and Space > Straight edge & compass constructions

### Curvy Areas

##### Stage: 4 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

### Squirty

##### Stage: 4 Challenge Level:

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

### Triangle Midpoints

##### Stage: 4 Challenge Level:

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

### Cool as Ice

##### Stage: 3 and 4 Challenge Level:

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

### Flip Your Mat!

##### Stage: 2 and 3 Challenge Level:

What shape and size of drinks mat is best for flipping and catching?

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### Moving Squares

##### Stage: 4 Challenge Level:

How can you represent the curvature of a cylinder on a flat piece of paper?

### Close to Triangular

##### Stage: 4 Challenge Level:

Drawing a triangle is not always as easy as you might think!

### Folding Fractions

##### Stage: 4 Challenge Level:

What fractions can you divide the diagonal of a square into by simple folding?

### Golden Trail 1

##### Stage: 3, 4 and 5 Challenge Level:

A first trail through the mysterious world of the Golden Section.

### Mathematical Patchwork

##### Stage: 2 and 3

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

### Half a Triangle

##### Stage: 4 Challenge Level:

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

### Three Tears

##### Stage: 4 Challenge Level:

Construct this design using only compasses

### Yin Yang

##### Stage: 2 Challenge Level:

Can you reproduce the Yin Yang symbol using a pair of compasses?

### Pentabuild

##### Stage: 5 Challenge Level:

Explain how to construct a regular pentagon accurately using a straight edge and compass.

### Two Points Plus One Line

##### Stage: 4 Challenge Level:

Draw a line (considered endless in both directions), put a point somewhere on each side of the line. Label these points A and B. Use a geometric construction to locate a point, P, on the line,. . . .

### Golden Construction

##### Stage: 5 Challenge Level:

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

### Circle Scaling

##### Stage: 4 Challenge Level:

You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3.

### Folding Squares

##### Stage: 4 Challenge Level:

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

### The Medieval Octagon

##### Stage: 4 Challenge Level:

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

### Pareq Exists

##### Stage: 4 Challenge Level:

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

### Pentagon

##### Stage: 4 Challenge Level:

Find the vertices of a pentagon given the midpoints of its sides.

### Kissing

##### Stage: 5 Challenge Level:

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?