if the base of an isosceles triangle is produced on both sides, prove that the exterior
angles so formed are equal to each other.
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Maths
The Triangle and Its Properties
Isosceles and Equilateral Triangles
If the base of an isosceles...
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Asked on January 17, 2020 by
Sulekh Sai
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
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Let ABC be an isosceles triangle with base BC and equal sides AB and AC.
Then, ∠ABC=∠ACB i.e., ∠B=∠C.
Now,
∠ADB+∠ABC=180
∘
and ∠ACB+∠ACE=180
∘
⇒∠ADB=180
∘
−∠B and ∠ACE=180
∘
−∠C
⇒∠ADB=180
∘
−∠B and ∠ACE=180
∘
−∠B
⇒∠ADB=∠ACE
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hence proved
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