Question

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

Answer 1

Here is your answer

Given= AD=DE

1) in triangle ABD and triangle ECD

Angle 1 = angle 2 ( vertically opposite angle)

BD=DC (given)

AD=DE (given)

Triangle ABD is congruent to triangle ECD by (SAS)

2). AB=EC (CPCT)

3) AB|| EC

Angle 3= angle 4 (CPCT)

Alternate interior angles are equal.

AB|| EC