Question

seg
AABD is a triangle in whinh La=90% and
ACI Seg BD show that got his
J AB2= BC XBD ),
U] AD = BD XCDI
13] AZ = BC XCD.
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Answer 1

Answer:

$Data: In ∆ABD, ∠A = 90°,  AC ⊥ BD.  To Proved: AB2 = BC.BD  (ii) AC2 = BC.DC  iii) AD2 = BD.CD  (i) AB2 = BC.BD  ∆ACB ~ ∆BAD (. Theorem7) ∴ ABBD=BCABABBD=BCAB ∴ AB2 = BC × BD.  (ii) AC2 = BC.DC  ∆BCA ~ ∆ACD ∴ ABAD=ACCD=BCACABAD=ACCD=BCAC  ∴ AC × AC = BC × CD  ∴ AC2 = BC × CD  (iii) AD2 = BD.CD  ∆ACD ~ ∆BAD ∴ ADBD=CDAD=ACABADBD=CDAD=ACAB ∴ AD × AD = BD × DC  ∴ AD2 = BD × Dc$