state and prove pethocarastherom
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Pythagoras theorem
In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of other two sides
Given :
△ABC right angles at B
To prove : AC
2
=AB
2
+AC
2
Construction : Draw DB⊥AC
Proof: Since BD⊥AC
△ADB∼△ABC∣△BDC∼△ABC
Since sides of similar triangles are in same ratio ∣ since similar triangle sides are in same ratio then
AB
AD
=
AC
AB
∣
BC
CD
=
AC
BC
AD.AC=AB
2
−−−−−−(1) ∣ AC.CD=BC
2
−−−−−−−(2)
add (1) and (2)
AD.AC+CD.AC=AB
2
+BC
2
AC(AD+DC)=AB
2
+BC
2
AC×AC=AB
2
+BC
2
AC
2
=AB
2
+BC
2
Hence proved
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