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  1. ABCD is an isosceles trapezium with AB || CD.
  2. ABCD is an isosceles trapezium with AD || BC. 
  3. ABCD is a kite with AB = AD.
  4. ABCD is a kite with AB = BC.
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Option 2 : ABCD is an isosceles trapezium with AD || BC. 

Given:

ABCD is a quadrilateral in which ∠A = ∠D and ∠B = ∠C.

Calculation:

Isosceles trapezium means bases of the trapezium are parallel and legs are equal.

∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠A + ∠B + ∠B + ∠A = 360° (As ∠A = ∠D and ∠B = ∠C)

⇒ 2∠A + 2∠B = 360° 

⇒ ∠A + ∠B = 180° 

If the sum of the interior angles on the same side of transversal is 180°. Then, the given lines are parallel. Hence, AD || BC.

∴ ABCD is an isosceles trapezium with AD || BC.

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