KS3 SAT pythagoras questions

ancient Chinese maths in right angled triangles

a ppt gives the problems and suggests approaches to each problem

there are 24 problems on this 'Gougou' topic
the first 10 are here (the rest are included on the ppt)

I have changed problems 7 and 8 to involve more manageable numbers
(my apologies)

pythagoras (CBSE-like) questions

these questions are from or are similar to those set in the CBSE (India) Y10 papers

the top left question leads to the cosine rule

using cos(180 - B) =  - cos B

 printable versions:

equable right angled triangles

not using pythagoras

working out the radius of the incircle

three little triangles sum to the large one

an alternative method, using pythagoras, to find the radius of the incircle

proving that there are just two right angled equable triangles with integer lengths

two of the possible values duplicate the other two

equable isosceles triangles

the area value = perimeter value
for isosceles triangles (including an equilateral triangle, in Q2) with integer heights

this work involves: surds,
rationalising (simple) denominators
and pythagoras

three triangles sum to the large (isosceles) triangle

and 2a + 2c = ah since P = A

triple triangle lengths

a ppt is here

grid triangles and pythagoras

advanced level students (those who have covered the expansion of tan(A + B))

might like to think why it is impossible to draw an equilateral triangle joining grid points on square grid paper
[due to the irrationality of tan 60]