In a trapezium ABCD with AB ║ CD, it is given that AD is not parallel to BC. Is ΔABC ≅ ΔADC? Give reasons.

Consider a trapezium ABCD, it is given that

AB||CD and the AD is not parallel to BC.

From the figure, we can say the similarities of ΔABC and ΔADC.

⇒ AC = AC (Common side)

⇒ ∠A = ∠C (Alternate angles on opposite sides of traversal line are equal)

⇒ ∠B≠∠D (One angle is obtuse and other is acute)

⇒ AB≠CD (From the figure)

From the above conclusions, we can say that any of the property like SSS, SAS, ASA is not satisfied. So, we can conclude that,

ΔABC is not congruent toΔADC.