Prove that the lengths of the diagonals of an isosceles trapezoid are equal

AD || BC 
• AB = CD 
• ∠BAD = ∠CDA (a given condition ∵ ABCD is an isosceles trapezium) 

The diagonals AC and BD create two ∆'s: ∆ABD, and ∆ACD 

The two ∆'s are congruent (SAS).  
 
(S): AB = CD 
(A): ∠BAD = ∠CDA 
(S): AD = DA (common side) 

The corresponding sides of the two ∆'s, BD and AC, are also congruent. 
(the two diagonals of the trapezium/trapezoid)