Fill in the blanks so that the following statements are true:

In ΔABC, m∠B = 90 and is an altitude. The correspondence BDA ↔ _____ between ΔBDA and ΔBDC is a similarity.

We have

Given: In ∆ABC,

∠ABC = ∠ADB = ∠BDC = 90°

In ∆BDA and ∆CDB,

∠BDA = ∠CDB = 90°

∠ABD = ∠BCD [measure of both being equal, i.e., (90° - m∠A)]

This can be explained as,

In ∆BDA, by angle sum property of triangle,

∠BDA + ∠DAB + ∠ABD = 180°

⇒ 90° + ∠A + ∠ABD = 180° [∵, ∠BDA = 90° & ∠DAB = ∠A]

⇒ ∠ABD = 180° - 90° - ∠A

⇒ ∠ABD = 90° - ∠A …(i)

Similarly, in ∆ABC by angle sum property of triangle,

∠ABC + ∠BAC + ∠BCA = 180°

⇒ 90° + ∠A + ∠BCD = 180° [∵, ∠ABC = 90°, ∠BAC = ∠A & ∠BCA = ∠BCD (from the figure)]

⇒ ∠BCD = 180° - 90° - ∠A

⇒ ∠BCD = 90° - ∠A …(ii)

By equations (i) and (ii), we get

∠ABD = ∠BCD

Hence, by AA corollary the correspondence BDA ↔ CDB is similarity between ∆BDA and ∆BDC.

Thus, the answer is CDB.