Help me prove

(a) x⁰=1
Verification
Taking log both sides
0.logx=log1
Which is true.Hence the given relation is also true.

Too easy Arvind... i didn't see it before

1> x⁰ = x^{(m - m)} = x^m.x^-m = x^m/x^m = 1

or, x⁰ = 1 Done..!!

2> IF two triangles are equiangular that means both of them are similar by (AAA criterion) and so, their sides will be proportional (by the definition of similar triangles)

well one more thing ....

Did you know that,

In two triangles if two corresponding sides are equal and angles excluding them are equal then both of them are congruent.

i.e., Did u know bout the SSA criterion?

well it is... check for my previous posts.... u'll get the proof !!

sorry but i added something more than u asked :D

@rahul
AIR or TV pe announce karwa de SSA[3]
just kidding

HA HA HA

b) its one of the euclid's elements

http://www.cut-the-knot.org/pythagoras/EuclidRef_VI.shtml

Just see the second question in your 9th standard state syllabus maths textbook.{theorem}

i am not from 9th class @aravind