# In a right ∆ABC,

It is given in the question that,

In right triangle ABC, B = 90o

Also D is the mid-point of AC

ADB = BDC (BD is the altitude)

BD = BD (Common)

So, by SAS congruence criterion

A = C (CPCT)

As, B = 90o

So, by using angle sum property

A = ABD = 45o

Similarly, BDC = 90o (BD is the altitude)

C = 45o

DBC = 45o

ABD = 45o

Now, by isosceles triangle property we have:

BD = CD and

AS, AD + DC = AC

BD + BD = AC

2BD = AC

BD =

Hence, proved

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