$In the figure, △ A B C is an equilateral triangle with each side measuring 6 cm. If AD bisects ∠ B A C, then what is the value of BD in cm?$
3

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Solution

The correct option is A 3
$In △ A B D and △ A D C$ ,

$B A = A C [△ A B C is equilateral]$
$∠ B A D = ∠ D A C [AD bisects ∠ B A C]$
$A D = A D [Common side]$

$△ A B D ≅ △ A D C (SAS rule)$

$So, B D = D C [CPCT]$

Hence,

$B D = \frac{6 c m}{2} = 3 c m$

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Similar questions

In the figure, △ A B C is an equilateral triangle with each side measuring 6 cm. If AD bisects ∠ B A C, then what is the value of BD in cm?

In the given figure, if $A D ⊥ B C$ and BD = DC, then AD bisects $∠ B A C$ .

△ A B C

A D ⊥ B C

A D^{2} = 3 B D^{2}

A B C

A B = A D

D

B D = C D

A D

∠ A

∠ D

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