Question

prove that the diagonals of a isosceles trepezium are equal?

Answer 1

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/)  

Hope this helps! Cheers! :)  

Answer 2

Answer:

Given: ABCD is an isosceles trapezium.

To Prove:

∠A = ∠B

Construction: Join the diagonal BD and AC.

Proof : In ∠ACB and ∠BDA

(1) BC=AD (Isosceles trapezium)

(2)AC=BD (Isosceles trapezium)

(3) AB=AB (Common side)

ACB ≅ △ BDA (SSS postulate)

∠A =∠B (Congruency property)