Question

Prove that in isosceles trapezium diagonals are equal

Answer 1

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/)