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SAS Criteria for Congruency

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Question 1
In quadrilateral ACBD, AC = AD and AB bisects $∠$ A (See the given figure). Show that $Δ A B C ≅ Δ A B D .$ What can you say about BC and BD?

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Solution

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

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SAS Criteria for Congruency

Standard VII Mathematics

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