Is,
BD = CE
State whether the above statement is true or false.

True

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False

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Solution

The correct option is A True
Given: AB = AC
$∠ A B C = ∠ A C B$ (Isosceles triangle property)
$∠ D B C = ∠ E C B$ (Given)
hence, $∠ D B C - ∠ A B C = ∠ E C B - ∠ A C B$
Thus, $∠ D B A = ∠ E C A$
In $△ A B D$ and $△ A C E$
$∠ D B A = ∠ E C A$ (Proved above)
$A B = A C$ (Given)
$∠ D A B = ∠ E A C$ (Vertically opposite angles)
Thus, $△ A B D ≅ △ A C E$ (SAS rule)
Hence, $B D = C E$ (Corresponding sides)

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