Question

In the right triangle ABC, right angled at C, M is the mid-point of

hypotenuse AB. C is joined to M and produced to a point D such that

DM=CM. Point D is joined to point B. Show that AMC ≅ BMD

D A

M

B C​

Answer 1

BM=AM

And also it is the mid point of DC then 

DM=MC

And AC=DB (same length)

∴Therefore we can say that

∴△AMC≅△BMD