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

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Solution

In the given figure,

In $Δ A B C,$

AB = AC and DB = DC

In $Δ A B C,$

$∵ A B = A C$

$∴ ∠ A C B = ∠ A B C$ ...(i)

(Angles opposite to equal sides)

Similarly, in $Δ D B C,$

DB = DC

$∴ ∠ D C B = ∠ D B C$ ...(ii)

Subtracting (ii) from (i)

$∠ A C B - ∠ D C B = ∠ A B C - ∠ D B C$

$\Rightarrow ∠ A C D = ∠ A B D$

$∴ R a t i o ∠ A B D : ∠ A C D = 1 : 1$

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