Symmetriangle
Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?
How many more triangles need to be shaded to make the pattern have a line of symmetry?
Image
![Symmetriangle Symmetriangle](/sites/default/files/styles/large/public/thumbnails/content-id-2518-Triangle%252520S.gif?itok=vXMUizYi)
The figure shows an equilateral triangle divided into small equilateral triangles, all equal.
What is the lowest number of small triangles which must now be shaded to produce a figure which has a line of symmetry?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Image
![Symmetriangle Symmetriangle](/sites/default/files/styles/large/public/thumbnails/content-id-2518-Triangle%252520S%252520s.gif?itok=hHwCbw7x)
Answer: 3
Selecting the dotted line as the line of symmetry, symmetry can be obtained by shading 3 more triangles.
The other two possible lines of symmetry would require 5 and 6 more shaded triangles.