Question

∆ABC is an isosceles triangle with AB = AC.side BA is produced to D such that AB = AD. prove that ∠BCD is a right angle.​

Answer 1

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Answer 2

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$\huge{\underline{\underline{\sf{\orange{</p><p>Question:-}}}}}$

∆ABC is an isosceles triangle with AB = AC.side BA is produced to D such that AB = AD. prove that ∠BCD is a right angle.

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$\huge{\underline{\underline{\sf{\orange{</p><p>Solution:-}}}}}$

${\blue{\sf\underline{Given}}}$

A ∆ABC in which AB = AC and side BA is produced to D such that AB = AD.

${\red{\sf\underline{To\:Prove}}}$

∠BCD = 90° .

${\pink{\sf\underline{Construction}}}$

produce BA to D such that BA = AD .

Join DC.

${\green{\sf\underline{proof}}}$

$ab \: = AC \: and \: AB = AD \: ⇒ AD \: = AC \\ now \: AB \: = AC ⇒ \angle \: ABC = \angle \: ACB \\ AD = AC ⇒ \angle \: ADC = \angle \: ACD. \\ \therefore \: \angle \: Abc + \angle \: ADC = \angle \: ACB + \angle \: ACD. \\ ⇒ \angle \: ABC + \angle \: ADC = \angle \: BCD \: \: \: \: (\angle \: ACB + \angle \: ACD = \angle \: BCD) \\ ⇒ \angle \: ABC + \angle \: ADC + \angle \: BCD = 2\angle \: BCD \\ \: \: \: \: \: \: \: (adding \: \angle \: BCD \: on \: both \: sides) \\ ⇒ 2\angle \: BCD = 180\degree \: \: \: (\therefore\: sum \: of \: the \: \triangle \: BCD \: \: is \: 180\degree) \\ ⇒ \angle \: BCD = 90\degree.$

Hence,∠BCD is a right angle.

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