Question

prove that the diagonals of an isosceles trapezium are equal

Answer 1

The diagonals are also of equallength. The base angles of anisosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base).

Answer 2

HEY DEAR....
HERE'S YOUR ANSWER ⬇
Consider the isosceles trapezium/trapezoid ABCD, where: 

• 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). 

Justification? 
• (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, as required/) 
Any doubts, please ask me in the comments.
HOPE YOU FIND IT HELPFUL :)
#LB ;)