If a side of a triangle is produced then the exterior angle so formed is equal to the sum of the two interior opposite angles. Prove.
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Let the angles of the triangle be a, b, c.
Let the exterior angle be d (exterior angle of c).
c+d=180° (linear pair)
c=180°-d.............( Eq. 1)
a+b+c=180° (angle sum property)
Substituting the value of c from eq. 1,
a+b+180°-d=180°
a+b=180°-180°+d
a+b=d
Hence proved.
Answered by
287
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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