Answer: ASA postulate
Step-by-step explanation:
According to the ASA (Angle-Side-Angle) postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent to each other. '
Here Given: ABCD is a parallelogram
That is, AB ║ CD and AD ║ BC
We have to prove that:The parallelogram ABCD has two pairs of opposite sides equal, that is, AB ≅ CD and AD ≅ BC.
Here BD is the diagonal of the parallelogram ABCD ( shown in the below figure)
Thus, In Δ ABD and Δ CBD
∠ABD ≅ ∠CDB ( alternative interior angles made on parallel lines by the same transversal BD)
BD ≅ BD ( Reflexive )
And, ∠ADB ≅ ∠CBD ( alternative interior angles made on parallel lines by the same transversal BD)
Here, Two angles and the included side of triangle ADB are congruent to two angles and included side of traingle BCD.
Therefore, By ASA postulate of congruence,
Δ ABD ≅ Δ CBD
Thus, By CPCTC, AB ≅ CD and AD ≅ BC.
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