Question

ABC is a right triangle with AB = AC. If bisector of ∠A meets BC at D,then prove that BC = 2AD​

Answer 1

Step-by-step explanation:

ABC is a right triangle with AB = AC. If bisector of ∠A meets BC at D,then prove that BC = 2AD

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Answer 2

Step-by-step explanation:

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${\tt{In Δ , ABC right angled at A and AB = AC }}$

→_→

${\tt{Hence ∠ A = ∠ B}}$

${\tt{We know that Sum of angles of a triangle = 180º }}$

→_→

${\tt{∠A+ ∠B+ ∠C=180º}}$

${\tt{90º+∠B+∠B=180º}}$

${\tt{2∠B=180º -90º}}$

${\tt{2∠B=90}}$

${\tt{∠B=45º…………………..(i)}}$

${\tt{ALSO , AD is the bisector of BAC}}$ 

${\tt{So , ∠BAD = ∠CAD = 90º/2 = 45º ………….(ii)}}$

${\tt{∠BAD = ∠ABC}}$

${\tt{SO, AD = BD ………(iii)}}$

${\tt{Similarly angle CAD = angle ACD }}$

${\tt{So, AD = DC …………..(iv)}}$

${\tt{adding equation (iii) and (iv)}}$

☞￣ᴥ￣☞

${\tt{We will get, AD + AD = BD+DC </p><p>2AD = BC}}$

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