In the given figure, AB $=$ AC, DB $=$ DC then $∠$ ABD $= ∠$ ACD.

True

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False

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Solution

The correct option is A True
In \Delta ABC$
$A B = A C$
$\Rightarrow ∠ A B C = ∠ A C B$ (i)
In $Δ B D C$
$B D = D C$
$\Rightarrow ∠ D B C = ∠ D C B$ (ii)
(i) - (ii)
$∠ A B C - ∠ D B C = ∠ A C B - ∠ D C B$
$∠ A B D = ∠ A C D$

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Similar questions

∠ A B D = ∠ A C D

In the figure, AB = AC and DB = DC, find the ratio $∠ A B D : ∠ A C D .$

In the given figure, $A B = D B$ and $A C = D C$ . If $∠ A B D = 58^{\circ}$ ,

$∠ D B C = (2 x - 4)^{\circ}$ , $∠ A C B = y + 15^{\circ}$ and
$∠ D C B = 63^{\circ}$ , find the values of $x$ and $y$

∠ D A C = ∠ A B D, A B = 20, A D = 10

A C = 12

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