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Answer: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Step-by-step explanation:
Given : ABCD is a parallelogram.
That is, AB ║ CD and AD ║BC
We have to prove that: AB≅CD and AD≅BC
Proof:
Construct diagonal AC in the parallelogram ABCD.
Since, AC ≅ AC ( reflexive)
∠ BAC ≅ ∠ DCA ( By the alternative interior angle theorem)
∠ BCA ≅ ∠ DAC ( By the alternative interior angle theorem)
⇒ Δ BCA ≅ Δ DAC ( By ASA congruence postulate )
⇒ AB≅CD as well as AD≅BC ( BY CPCTC )
Thus, the opposite side of the parallelogram are congruent.
