Data Sufficiency

Can you pls help with your explanation? thanks!

Statement 1 is sufficient.
Diagonals divide a parallelogram into 2 triangles of equal areas.

Unfortunately the answer seems different.


Is anyone else able to help us?

Let me know in case of any errors in below logic:
Note that for a triangle: Area = (base * height) /2
hence for any triangle the area will be constant so long as the base & height (vertical distance of top vertex from base) are constant
Which means that for a given base & height the area will be the same even if triangle is equilateral or isoceles or scalene.
1. same area does not mean that the side are of same measures or angles are in similar ratios. Hence Not Sufficient.
2. QR = RS : QRS is isoceles. However the other triangle has no restriction. Hence Not Sufficient.

Taken together: areas are same & QRS is isoceles, however, the triangle PQS may or may not be isoceles.

Hence answer should be E.

thanks - answer is E.