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?
Age
11 to 14
Challenge level
Problem
Image
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.
Student Solutions
Image
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.