Question

In a triangle ABC  , D is mid - point of BC ; AD is produced upto E so that DE = AD prove that :

Easy

Solution

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Given ; A in which  D is the mid - point of BC
AD is produced to E so that DE = AD
We need to prove that
AB = EC
AB \\ EC
In and
BD = DE                                                        [D is the midpoint of BC]
                   [Vertically opposite angles]
AD = DE                                                         [Given]
By Side - Angle - Side criterion of congruence we have 

Also ,                  [The corresponding parts of congruent triangles are equal]


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