Other tags that relate to Pareq Exists
Constructions. Generalising. Visualising. Regular polygons and circles. Mathematical reasoning & proof. Pythagoras' theorem. Similarity and congruence. Triangles. Creating and manipulating expressions and formulae. Circle properties and circle theorems.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.
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?
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.
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?
Folding Fractions
Age 14 to 16 Challenge Level:
What fractions can you divide the diagonal of a square into by simple folding?
Circle Scaling
Age 14 to 16 Challenge Level:
Describe how to construct three circles which have areas in the ratio 1:2:3.
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?
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.
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,. . . .
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 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?
Close to Triangular
Age 14 to 16 Challenge Level:
Drawing a triangle is not always as easy as you might think!
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?
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.