#1**+1 **

Construct a circle of any radius and let chords AB and CD be parallel

Join AD, BC and let E be the intersection of these chords

Now....because AB and CD are parallel and AD and BC are transversals, then angle BAE = angle CDE

And angle ABE = angle DCE for the same reason

And angle ABE = angle CDE because they intercept the same arc

And angle BAE = angle DCE for the same reason

Therefore....angle CDE = angle DCE...so....in triangle CED.....CE = DE

And....angle BAE = angle ABE....so..in triangle AED.....AE = BE

Therefore....AE + DE = CE + BE

And....AE + DE = AD

And CE + BE = BC

So....AD = BC

CPhill Jun 4, 2019