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  • 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 DM = CM. Point D is joined to point B (see Fig). Show that: (iii) ∆ DBC ≅ ∆ ACB

8.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:  \small \Delta DBC\cong \Delta ACB                                                                     

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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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Sanket Gandhi

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