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Question

Identify the number of triangles similar to ΔABC if B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC.


  1. 2

  2. 3

  3. 4

  4. 6


Solution

The correct option is C

4


BD is the perpendicular drawn to the hypotenuse.
InΔABD & ΔBDC
ADB=BDC=90
A=DBC(Since in ΔBDC,DBC=90C 
and In ΔABCA=90C)
,ΔADBΔBDC by AA-similarity
Similarly, in ΔBDC,DE is the perpendicular drawn to the hypotenuse BC.
In ΔBDE & ΔBDC
BED=BDC=90
DBC=DBC (Common Angle)                    
,ΔBEDΔBDCby AA-similarity
Hence, ΔADBΔBDCΔBEDΔDECΔABC.
Therefore, there are 4 triangles similar to ΔABC.\)

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