Prove that a triangle must have at least two acute angles.
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●◆Ekansh Nimbalkar◆●
hello friend of here is your required answer
hello friend of here is your required answer
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sum of angles of triangle = 180*( always)
Lets assume that only one angle have to be acute (contradiction)= less than 90*
the other two angle will have to be right or obtuse (90* and greater than 90)
lets take a contradiction that both are of 90*
the the 3rd angle (x) which is an acute angle will be -
180*= 90*+90*=X
X = 180*- 90*-90*
X= 0
we know that an angle of a triangle cannot be 0
so therefore our contradiction is wrong
so we can say that
.. we can prove that a triangle must have atleast two angles acute..
Lets assume that only one angle have to be acute (contradiction)= less than 90*
the other two angle will have to be right or obtuse (90* and greater than 90)
lets take a contradiction that both are of 90*
the the 3rd angle (x) which is an acute angle will be -
180*= 90*+90*=X
X = 180*- 90*-90*
X= 0
we know that an angle of a triangle cannot be 0
so therefore our contradiction is wrong
so we can say that
.. we can prove that a triangle must have atleast two angles acute..
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