Which of the following is incorrect for the following figure?

AB = BC

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\neq

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AD = BC

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AB = DC

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Solution

The correct option is A AB = BC
Consider $△ A D B$ and $△ C B D$ ,
$∠ A B D = ∠ C D B$ ..... (given)
$∠ A D B = ∠ C B D$ ..... (given)
BD = BD .... (Common side)

Therefore, $△ A D B ≅ △ C B D$
by ASA criterion for congruency of triangles.

$\Rightarrow$ AB = CD and AD = CD . . . (corresponding parts of congruent triangle)
$\Rightarrow$ AB $\neq$ BC (non-corresponding sides)

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