Q5 of 13 Page 96

If we produce the base of an isosceles triangle in both sides then two exterior angles formed. Let’s prove that they are equal in measurement.


Let an isosceles ΔEFG in which the side FG is extended on both sides to form two exterior angles.


EF=FG


So, ∠EFG=∠EGF…………(1)


As we know that sum of two interior angles is equal to the exterior angle of a triangle.


∠EFI=∠EFG+∠E…….(2)


∠EGJ=∠EGF+∠E…….(3)


Now, Subtracting equation (2) from (3)


∠EGJ-∠EFI=∠EGF+∠E-∠EFG-∠E


⇒ ∠EGJ-∠EFI=∠EGF -∠EFG=0 (from (1))


⇒ ∠EGJ-∠EFI=0


⇒ ∠EGJ=∠EFI


Proved.


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