8.(iii) In 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 \small DM=CM. Point D is joined to point B (see Fig.). Show that: 

 (iii) \small \Delta DBC\cong \Delta ACB                                                                                                 

                             

Answers (1)

Consider \Delta DBC  and  \Delta ACB,

(i)          BC\ =\ BC          (Common in both the triangles)

(ii)   \angle ACB\ =\ \angle DBC                    (Right angle)

(iii)         DB\ =\ AC            (By c.p.c.t. from the part (a) of the question.)

Thus SAS congruence we can conclude that :  

                                                      \small \Delta DBC\cong \Delta ACB

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