​lines, rotations, distances, expressions

Here's the first one

Actually....angles  A and C are equal

And angles  E and C are equal

So....by AA conguency.....triange ACB is similar to triangle ECD

So....angle  BAC = angle DEC...and these are opposite imterior angles 

And angle CBA = angle EDC...and these are oppositie interior angles

And AE and BD are transversals cutting AB and DE

But...when transversals cutting two line segments make opposite interior angles equal....the segments are parallel

So   AB ll DE