Skip over navigation
Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Close to Triangular
Preveina from Crest Girls' Academy made a start on this problem:
For three points, there are always infinitely many such triangles because every time you extend the length of the lines in a triangle you will be making a new point; by doing this you'll be producing unique triangles every time. This then leads on having infinity triangles made.
The picture below shows a sequence of triangles - the black lines pass through two of the points, and a variety of lines can pass through the third point, extending one of the lines in the original triangle.
Preveina went on to show some examples of configurations of four and five points where a triangle could be drawn.
To consider whether all configurations are possible, consider the set of points below:
Can you find a way to draw a triangle passing through all four points? Can you convince yourself it is impossible?
Mathematical reasoning & proof
Cartesian equations of lines
Making and proving conjectures
Straight edge & compass constructions
Summation of series
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Register for our mailing list
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the
Millennium Mathematics Project