ABC is a triangle in which ∠ABC = 90°. BD is perpendicular to AC. Which of the following is TRUE?
I. Triangle BAD is similar to triangle CBD.
II. Triangle BAD is similar to triangle CAB.
III. Triangle CBD, is similar to triangle CAB.

Solution (By Examveda Team)

In ΔBAD and ΔBDC
∠BDA = ∠BDC   (Each 90°)
If ∠C = 30°
Then ∠A = 60°
Also ∠ABD = 30°
∠BCD = ∠ABD
ΔBAD ∼ ΔBDC . . . . . (i)
In ΔBAD and ΔCAB
∠BDA = ∠ABC   (Each 90°)
∠BAD = ∠BAC   (common)
ΔBAD ∼ ΔCAB . . . . . (ii)
Similarly ΔCBD ∼ ΔCAB . . . . . (iii)
All conditions are true.