In
△AMC and
△BMDAM=BM ....Since M is the midpoint of the hypotenuse AB
CM=DM .... Given
∠AMC=∠BMD ..... Vertically opposite angles
∴AMC≅BMD .... SAS Rule
Option B:
∠ACM=∠BDM .... cpct
But these are the alternate angles and they are equal.
AC||BD
Now, AC||BD and a transversal BC intersects, then
∠DBC+∠ACB=180o
The sum of consecutive interior angles on the same sides of the tranversal is 180o.
⇒DBC+90o=180o
⇒DBC=90o
∴∠DBC is a right angle.