Given that ABCD is a trapezium,
AB∥CD and AD=BC
To prove: ∠A=∠B
Construction: Draw CE∥AD and extend AB to intersect CE at E.
Poof: As AECD is a parallelogram.
By constriction, CE is parallel to AD and AE is parallel to CD,
∴AD=EC
But, AD=BC (Given)
∴BC=EC
⇒∠3=∠4 (Angle opposite to equal side are equal)
Now, ∠1+∠4=1800 (consecutive interior angle of parallelogram )
And ∠2+∠3=1800 (linear pair )
⇒∠1+∠4=∠2+∠3 ⇒∠1=∠2∵∠3=∠4 (so get cancelled with each other )
⇒∠A=∠B
Hence, proved .