prove that if sides of a triangle is produced, the exterior angle so formed is equal to the sum of opposite interior angles.
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use angle sum property of triangle and linear pairs of triangle
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Statement : If side of a triangle is produced, then the exterior angles so formed is equal to the sum of the two interior opposite angles.
Given : A triangle ABC with interior angles x , y and z and exterior angle 'e'.
To prove : e = x + y
Proof :
In the figure, :
x + y + z = 180°.... (i) [Angle sum property]
e + z = 180 ° ........ (ii) [Linear pair]
On camparing equation ( i ) and ( ii )
x + y + z = e + z
Therefore, x + y = e
Hence, it is proved.
Given : A triangle ABC with interior angles x , y and z and exterior angle 'e'.
To prove : e = x + y
Proof :
In the figure, :
x + y + z = 180°.... (i) [Angle sum property]
e + z = 180 ° ........ (ii) [Linear pair]
On camparing equation ( i ) and ( ii )
x + y + z = e + z
Therefore, x + y = e
Hence, it is proved.
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