prove that triangle must have at least two acute angles
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sum of angles of triangle = 180*
Lets assume that only one angle have to be acute ei. <90*
Then the other two angle will have to be right or obtuse (90* and 90>)
lets assume that both are of 90* (lowest possibility)
the the 3rd angle (x) which is an acute angle will be -
180*= 90*+90*=X
X = 80*- 90*+90*
X= 0
we know that an angle of a triangle cannot be 0
hence our assumtion is proved wrong!
with this.. we can prove that a triangle MUST have atleast two angles acute....
....I hope this was helpful
Lets assume that only one angle have to be acute ei. <90*
Then the other two angle will have to be right or obtuse (90* and 90>)
lets assume that both are of 90* (lowest possibility)
the the 3rd angle (x) which is an acute angle will be -
180*= 90*+90*=X
X = 80*- 90*+90*
X= 0
we know that an angle of a triangle cannot be 0
hence our assumtion is proved wrong!
with this.. we can prove that a triangle MUST have atleast two angles acute....
....I hope this was helpful
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