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Lines in a Triangle

Question 7ABC...

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Question 7
ABC is a right angled triangle in which $∠ A = 90^{\circ} a n d A B = A C . F i n d ∠ B a n d ∠ C .$

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Solution

$I t i s g i v e n t h a t A B = A C \Rightarrow ∠ C = ∠ B (A n g l e s o p p o s i t e t o s i d e s a r e a l s o e q u a l) I n Δ A B C, ∠ A + ∠ B + ∠ C = 180^{\circ} (A n g l e s u m p r o p e r t y o f a t r i a n g l e) \Rightarrow 90^{\circ} + ∠ B + ∠ C = 180^{\circ} \Rightarrow 90^{\circ} + ∠ B + ∠ B = 180^{\circ} \Rightarrow 2 ∠ B = 90^{\circ} \Rightarrow ∠ B = 45^{\circ} ∴ ∠ B = ∠ C = 45^{\circ}$

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Lines in a Triangle

Standard VI Mathematics

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