Question

in the given figure ABC is a right triangle right angled at C M is the midpoint of hypotenuse a b c is 12 m and produced to a point D such that DM is equal to CM. D is joined to be so that a​

Answer 1

Given : M is mid point of AB

So, BM =AM

DM = CM

Proof:

In triangle AMC and BMD

AM = BM [ given ]

CM = DM [ given ]

<AMC= <BMD [ vertically opposite angle ]

AMC ~= BMD [ SAS congruence ]

Hence, first prove

If AMC ~= BMD
then, < MAC =< MDB
AC = BD

In triangle ABC and DBC
< BAC = <BDC [ proved above ]
AC. = BD[proved above ]
BC. = BC [ common ]
ABC ~= DBC [SSA congruence ]

Hence, second prove

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