Q7 of 47 Page 7

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal.

To prove: the exterior angles formed are equal.


i.e., ∠ADB =∠ACE


Proof: Let ABC be an isosceles triangle



Where BC is the base of the triangle and AB and AC are its equal sides.


ABC =ACB


∠B =∠C (Angle opposite to equal sides)


Now,


∠ADB +∠ABC = 180° (linear pair)


∠ACB +∠ACE =180° (linear pair)


∠ADB =180° -∠B


And


∠ACE=180° -∠C


∠ADB = 180° - ∠B


And


∠ACE=180° -∠B


∠ADB =∠ACE


Hence, proved


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