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.

i need the answer now!!!

Answer 1

Hope this answer will help you..

Answer 2

Ok First of all,,
As According to Question we find the figure as above..
Now in ∆ ABD and ∆ECD..
1. BD = CD........... as D is the mid point of BC,,
2. AD = ED.......... as given in Question,,
3. Angle ADB = Angle EDC ...... Vertically Opposite Angles.....
So bye SAS Criteria of Congruency....
∆ABD ≈ ∆ ECD.....

Now Second,,
to proove ; AB is parallel to EC...
for that,
in Question D is the mid point of AE as well as BC..
Or BC bisects AE or vice versa so it is clear that the figure form by joining ABEC is a Rhombus, Parallelogram Square orr a Rectangle....
And in all those shapes the opposite sides are parallel....
Hence AB is parallel to EC....
Thank you...