ratio and right angled triangles

the powerpoint is here

I think it might be easier to recognise similarity/enlargement in right angled triangles rather than rectangles

reasons for similarity can be articulated by considering the scale factors of enlargements

those who seek to use additive methods for ratios might appreciate that this doesn't work out too well

the link between equivalent ratios and straight line graphs can be explored
(as can tan (base angle), probably at a later stage)

it's not usually a good idea to ask which ratio is bigger - because they could be turned around

but, this question can be posed in the spirit of asking which is the better deal, £3 for 5 articles or £4 for 7 articles?

the steeper the line the bigger the ratio

which can also be appreciated by scaling the ratios