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By giving counter example show that the statement "If all the angles of a triangle are equal then the triangle is an obtuse angled triangle" is not true.

1 Answer

The given statement is
"If all the angles of a triangle are equal then the triangle is an obtuse angled triangle."
Let $ABC$ be a triangle in which all the angles are equal to $x.$ (say)
For any $\Delta$ the sum of the angles is equal to $180^\circ$.
$\Rightarrow\:\:x+x+x=180^\circ$
$\Rightarrow\:3x=180^\circ$ or $x=60^\circ$.
$\Rightarrow\: $ All the three angles are equal to $60^\circ$.
But in an obtuse angled $\Delta$, one angle is greater than $90^\circ$.
$\therefore$ $\Delta\:ABC$ cannot be obtuse angled $\Delta.$
Hence the given statement is false.
answered Jul 29, 2014 by rvidyagovindarajan_1
 

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