help me 2 prepare an good math project??

Question

1 to prove pythagoras theorum (activity method)
2 relatinship between area of simmilar trianges(activity mathod)

Answer 1

1. Go through any text book. Draw a right angled triangle ABC with
2. For two similar triangles ABC and XYZ the length of the corresponding sides are proportional. Let a, b, c be the sides of ABC corresponding to sides x, y, z of XYZ.
Then, a/x = b/y = c/z = constant, say k.
Now, area of triangle ABC is
A1 = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

Again, area of triangle XYZ is
A2 = sqrt[s'(s'-x)(s'-y)(s'-z)] where s' = (x+y+z)/2

Now, s = (a+b+c)/2 = (xk+yk+zk)/2 = k*(x+y+z)/2 = ks'

Again, A1 = sqrt[ks' (ks'-kx) (ks'-ky) (ks'-kz)]
= (k^2)*sqrt[s'(s'-x) (s'-y) (s'-z)]
= (k^2)*A2
or A1 = A2*k^2
Thus you obtain the relation between the area of the triangles.

Answer 2

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