$Δ$ ABC is an isosceles triangle in which AB $=$ AC. Show that $∠$ B $= ∠$ C.

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Solution

$W e g i v e n a n i s o s c e l e s t r i a n g l e, A B C i n w h i c h A B = A C . w e n e e d t o p r o v e t h a t ∠ B = ∠ C L e t u s d r a w t h e b i sec t o r o f ∠ A a n d l e t D b e t h e p o i n t s o f i n t e r sec t i o n o f t h i s b i sec t o r o f ∠ A a n d B C$ $(S e e F i g) I n t r i a n g l e, A B = A C (g i v e n) ∠ B A D = ∠ C A D (b y c o n s t r u c t i o n) A D = A D (c o m m o n) Δ B A D ≅ Δ C A D (b y S A S n e e d) ∴ ∠ B = ∠ C (C P C T) .$

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