Other tags that relate to Pareq Exists
Pythagoras' theorem. Similarity and congruence. Visualising. Creating and manipulating expressions and formulae. Constructions. Circle properties and circle theorems. Triangles. Generalising. Factors and multiples. Mathematical reasoning & proof.There are 22 results
Broad Topics > Transformations and constructions > Constructions
Pareq Exists
Age 14 to 16
Challenge Level
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Folding Fractions
Age 14 to 16
Challenge Level
What fractions can you divide the diagonal of a square into by simple folding?
Folding Squares
Age 14 to 16
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?
Circle Scaling
Age 14 to 16
Challenge Level
Describe how to construct three circles which have areas in the ratio 1:2:3.
Close to Triangular
Age 14 to 16
Challenge Level
Drawing a triangle is not always as easy as you might think!
Triangle Midpoints
Age 14 to 16
Challenge Level
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
The Medieval Octagon
Age 14 to 16
Challenge Level
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Curvy Areas
Age 14 to 16
Challenge Level
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
The Square Under the Hypotenuse
Age 14 to 16
Challenge Level
Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
The Farmers' Field Boundary
Age 11 to 14
Challenge Level
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Two Points Plus One Line
Age 14 to 16
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,. . . .
Half a Triangle
Age 14 to 16
Challenge Level
Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
Squirty
Age 14 to 16
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.
Moving Squares
Age 14 to 16
Challenge Level
How can you represent the curvature of a cylinder on a flat piece of paper?
LOGO Challenge 8 - Rhombi
Age 7 to 16
Challenge Level
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
LOGO Challenge 2 - Diamonds Are Forever
Age 7 to 16
Challenge Level
The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
Flip Your Mat!
Age 7 to 14
Challenge Level
What shape and size of drinks mat is best for flipping and catching?
Mathematical Patchwork
Age 7 to 14
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
Attractive Rotations
Age 11 to 14
Challenge Level
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Cool as Ice
Age 11 to 16
Challenge Level
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
NRICH is part of the family of activities in the Millennium Mathematics Project.