In quadrilateral ACBD, AC = AD and AB bisects $∠ A$ . Show that $△ A B C ≅ △ A B D$ . What can you say about BC and BD?

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Solution

Given:
$A C = A D ∠ C A B = ∠ D A B (∵ AB bisects ∠ A)$

$Consider △ A B C and △ A B D A C = A D (Given ) ∠ C A B = ∠ D A B (Given ) A B = A B (Common side ) By SAS Congruency, △ A B C ≅ △ A B D B C = B D (By CPCT)$

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In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?

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≅

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