Hi sana.noor,

Rahul has done a nice job of explaining this DS question.

For future reference, you have to be very careful with "pictures" in DS questions - in real basic terms, you CANNOT TRUST THE PICTURE.

In this question, it certainly appears that the 3 triangles are the same size, but WE CAN'T TRUST THE PICTURE. Thus, we need facts/data to prove if the two lines are parallel. This is a YES/NO question.

Fact 1: The triangle ACD is equilateral.

Here, we know that AD and CD are equal, but we don't know anything about AB and CE (and we don't know anything about the relative size of those other 2 triangles). Those line segments (AE and CE) will affect whether the two lines are parallel or not.
Fact 1 is INSUFFICIENT.

Fact 2: Triangles ABD and CDE are equilateral.

IF those two triangles are the exact same size, then the two lines are parallel

HOWEVER, if those two triangles are NOT the exact same size, then the two lines are NOT parallel.
Fact 2 is INSUFFICIENT.

Combining Facts, we know that all 3 triangles are equilateral AND have the same side lengths. This means that the two lines MUST be parallel.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich