Geometry

Question Analysis:
This advanced question tests understanding of the reflexive property in geometric proofs and its application to SSS congruence within quadrilaterals.

Key Concept Explanation:
SSS Congruence requires three pairs of congruent sides.
In quadrilateral ABCD:
AB ≅ CD (given)
AD ≅ BC (given)
AC is shared (reflexive property: AC ≅ AC).

Step-by-Step Solution:
Given:
AB ≅ CD
AD ≅ BC
Identify the third pair of sides:
Diagonal AC is common to both △ABC and △CDA.
By the reflexive property, AC ≅ AC.
Conclusion:
All three sides of △ABC correspond to and are congruent with those of △CDA.

Option Analysis:
A: Irrelevant. Perpendicularity does not contribute to side congruency.
C: Irrelevant. Angle congruency is not required for SSS.
D: Unnecessary. While true, it’s not ne...