In the given figure, AB = AC. Side BA is produced to D such that BA = AD. $△$ BDC is _______.

30º

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60º

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90º

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120º

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Solution

The correct option is C
90º

In $△$ ABC, AB = AC ..... (given)

$∠$ ABC = $∠$ ACB = $∠$ x (say) ....... (base angles of an isosceles $△$ )

In $△$ ACD, AC = AD ...(given, BA = AD and BA = AC)

$∠$ ADC = $∠$ ACD = $∠$ y (say) ....... (base angles of an isosceles $△$ )

In $△$ ADC,

x° + x° + y° + y° = 180° ...... (sum of angles of a $△$ )

2 (x° + y°) = 180°

x° + y° = 90°

$∠$ DCB = 90°

$△$ BDC is a right angle.

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In the given figure, AB = AC. Side BA is produced to D such that BA = AD. △BDC is _______.

In the given figure, AB = AC. Side BA is produced to D such that BA = AD. $△$ BDC is _______.