Question

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

Answer 1

ED is a straight line segment and B and C are points on it. 

⇒ ∠EBC=∠BCD=straight angle =180° 

⇒ ∠EBA+∠ABC=∠ACB+∠ACD 

⇒ ∠EBA=∠ACD+∠ACB-∠ABC 

⇒  ∠EBA=  ∠ACD              [from (1) ∠ ABC=∠ ACD]

⇒ ∠ABE= ∠ACD  

∴ Hence proved