Q. 225.0( 3 Votes )

# In the given figure, ABD is a right angled triangle being right angled at A and AD ⊥ BC. Show that:(i) AB2= BC.BD(ii) AC2 = BC. DC(iii) AB. AC. = BC. AD

(i) In ΔDAB and ΔACB

ADB = CAB [each 90°]

DAB = CAB [common angle]

DAB ~ACB [by AA similarity]

Since the triangles are similar, hence corresponding sides are in proportional.

AB2= BC×BD

(ii) In ACB and DAC

CAB = ADC [each 90°]

CAB = CAD [common angle]

ACB ~DAC [by AA similarity]

Since the triangles are similar, hence corresponding sides are in proportional.

AC2 = BC. DC

(iii) In part (i) we proved that DAB ~ACB

AB × AC = BC × AD

Hence Proved

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