In quadrilateral $A C B D, A C = A D$ and $A B$ bisects $∠ A$ . Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

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Solution

Given quadrilateral $A B C D$ ,

In $△ A B C$ and $△ A B D$ ,

$A C = A D$ (Given)

$∠ C A B = ∠ D A B$ ( $A B$ bisects $∠ A$ )

$A B = A B$ (Common)

$∴ △ A B C ≅ △ A B D$ (By SAS congruence rule)

$∴ B C = B D$ (By corresponding parts of congruent triangles are equal (CPCT))

$∴$ $B C$ and $B D$ are of equal lengths.

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