Question

In a triangle ABC , D is the mid-point of BC; AD is produced upto
E so that DE = AD.
Prove that :
i) triangle ABD and triangle ECD are congruent.
ii) AB = EC.
iii) AB is parallel to EC.

Answer 1

It is congruent by SAS congruency rule

ΔABD AND ΔECD

ANGLE D = ANGLE D (VOA )

AD = ED(Given in the question)

BD = CD (D is the midpoint of BC)

Therfore  by SAS congruency rule

ΔABD and ΔECD are congruent

Then by CPCT

AB = EC

As said angle d= angle d we can say that AB║EC

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