[Maths-Education] Ratio and Proportion

[Anne Watson]

Dave raises a point which has also puzzled me.   The nonsense is revealed 
if you consider two similar triangles drawn next to each other.   Comparing 
the sides doesn't fit with the "part to part" nor the "part to whole" 
definitions, so this comparison is neither ratio nor proportion.  So tuck 
the smaller triangle inside the larger so that they have a common 
vertex.  Then two pairs of sides can be compared part to part, but the 
third side still doesn't fit the Strategy guidelines!  Try again.   This 
time, think about comparing the three sides of each triangle to each other 
as a three-part-ratio (part to part to part???) , then the three-part 
ratios of both triangles are equal, but this is light-years away from what 
is presented in the Strategy.

Help!