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Question

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



A

2

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B

3

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C

4

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D

6

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Solution

The correct option is C

4


BD is the perpendicular drawn to the hypotenuse.
In ABD and BDC
ADB=BDC=90
A=DBC  [Since, in BDC, DBC=90C=A and in ABC, A=90C]

Therefore, ADBΔBDC  [by AA similarity]
Similarly, in BDC, DE is the perpendicular drawn to the hypotenuse BC.
In BDE and BDC
BED=BDC=90
DBC=DBC  [Common Angle]                   
Therefore, BEDBDC  [by AA similarity]
Hence, ADBΔBDCΔBEDΔDECΔABC.
Therefore, there are 4 triangles similar to ABC.


Mathematics

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