in the figure, Db is perpendicular to Bc and de is perpendicular to ab and ac is perpendicular to bc prove that be/ de = ac/bc.
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⌬ Correct Question:-
in the figure,DB is perpendicular to BC and DE is perpendicular to AB and AC is perpendicular to BC prove that BE/ DE = AC/BC.
⌬ Given:-
•In the given figure DB⏊BC; DE⏊AB and AC⏊BC
⌬ To Prove:-
•BE/DE=AC/BC
⌬ Proof:-
DB⏊BC
Therefore, ∠DBC=90⁰
==>∠DBE+∠ABC=90⁰ ____( 1 )
AC⏊BC
Therefore, ∠ACB=90⁰
==>∠ABC+∠BAC=90⁰ ____( 2 )
In view of (1) and (2)
∠DBE=∠BAC. ____( 3 )
In ΔDEB and ΔBCA
∠DEB=∠BCA [Each =90⁰]
∠DBE=∠BAC [From (3) ]
Therefore ,
ΔDEB∼ΔBCA. [ AA similarities]
Therefore,
BE/AC=DE/BC [ Corresponding sides of two similar triangles are proportional]
==> BE/DE=AC/BC
Hence, Proved
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