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Question
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?
Solution
Given: In quadrilateral ABCD, AC = AD and AB bisects ∠A.
To prove: △ABC ≌ △ABD
Proof: In △ABC and △ABD,
AC = AD ...[Given]
∠BAC = ∠BAD ...[∵ AB bisects ∠A]
AB = AB ...[Common]
∴ △ABC ≌ △ABD ...[By SAS congruence rule]
Hence, BC = BD ...[Corresponding parts of congruent triangles]
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