Answer:
Option 2. ΔBDA ∼ ΔACB is the right answer.
Explanation:
As we know if we have two triangles similar we have to prove the following conditions.
1) All angles of these two angles should be similar.
2) Opposite sides of the angles should be in the same ratio.
So in the given picture we see the three triangles Δabd, Δabc and Δadc.
Now in Δabc and Δadc there is no similarity in angles or sides therefore these triangles are not similar.
Now we compare ΔBDA and ΔACB.
∠DAB =∠ACB = 90°and ∠ABD is a common angle shared by these two triangles.
We know that if two angles of the given triangles are same then the third angles will be same.
Therefore ∠ADB =∠CAB
Now we can say that all angles of ΔBDA and ΔACB are similar.
Hence ΔBDA ∼ ΔACB is the right answer.