Justify the last two steps of the proof.

Question

Given: ABCD is a parallelogram.
Prove: ΔABC is congruent to ΔCDA

The figure shows parallelogram A B C D with diagonal A C.

ABDC is a parallelogram.
AB is congruent to DC and BC is congruent to DA
AC is congruent to CA
ΔABC is congruent to ΔCDA
Given
Opposite sides of a parallelogram are congruent.
_____________________?
_____________________?
(1 point)
Responses

Transitive Property of congruent; SAS
Transitive Property of Image with alt text: congruent ; SAS

Reflexive Property of congruent; SAS
Reflexive Property of Image with alt text: congruent ; SAS

Transitive Property of congruent; SSS
Transitive Property of Image with alt text: congruent ; SSS

Reflexive Property of congruent; SSS
Reflexive Property of Image with alt text: congruent ; SSS
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Answer 1

The last two steps of the proof are:

(1) Transitive Property of congruence; SAS (Side-Angle-Side): This step is justified because we are given that AB is congruent to DC and BC is congruent to DA. In addition, we know that AC is congruent to CA (Reflexive Property of congruence) and the included angle BAC is congruent to the included angle CAD (Alternate Interior Angles Theorem). Therefore, by the SAS congruence criterion, we can conclude that ΔABC is congruent to ΔCDA.

(2) Transitive Property of congruence; SSS (Side-Side-Side): This step is justified because we are given that AB is congruent to DC, BC is congruent to DA, and AC is congruent to CA. Therefore, by the SSS congruence criterion, we can conclude that ΔABC is congruent to ΔCDA.