In the given figure ,BD bisects angle ABC and angle ADC.Is triangle BAD congruent to triangle BCD?if so give reasons.Angle A and angle C is 90 degrees.

In ΔBAD and ΔBCD,

BD = BD (common)

∠BAD = ∠BCD = 90° (Given)

Now, BD bisects ∠ABC (Given),

⇒ ∠ABD = ∠CBD 

Thus, by AAS congruency criteria,

ΔBAD is congruent to ΔBCD.