If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
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.
Solution:
ED is a straight line segment and B and C an points on it.
∠EBC = ∠BCD = straight angle = 180°
∠EBA + ∠ABC = ∠ACB + ∠ACD
∠EBA = ∠ACD + ∠ACB - ∠ABC
∠EBA = ∠ACD [From (i) ABC = ACD]
∠ABE = ∠ACD
Hence proved