The triangles ΔABC ≅ ΔCDA are congruent in the given parallelogram according to the AAS axiom. By the two-column proof, we can verify this.
Statement Reason
AB║DC Given
(AC is the transversal)
∠BAC ≅ ∠ACD Alternative angles
∠B ≅ ∠D Opposite angles of a parallelogram are equal
AC ≅ AC Reflexive property
∴ ∠ABC ≅ ∠CDA AAS (angle-angle-side axiom)
If two triangles have two congruent angles and one side, then those triangles are said to be congruent by the AAS theorem.
Therefore, the triangles in the given parallelogram are congruent.
Learn more about the two-column proof for a parallelogram at the following link:
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