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

Answer :

(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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