![]() You can ask a new question or answer this question. We also know that AC is congruent to itself by the reflexive property of congruence.īy using the transitive property of congruence, we can conclude that ΔABC is congruent to ΔCDA. ![]() In this case, we know that AB is congruent to DC and BC is congruent to DA from the given information. To justify the last two steps of the proof, we need to use the congruence postulate of SAS (Side-Angle-Side). Recall: Based on the, CPCTE Theorem, if two triangles are congruent, all its corresponding sides and angles of both triangles are therefore congruent together. ![]() Using the SAS congruence criterion, if ABDC is a parallelogram and AC is congruent to CA, then we can conclude that triangle ABC is congruent to triangle CDA. The reasons that matches the statements in the two-column proof is shown in the table attached in the image below. The last two steps of the proof can be justified using the transitive property of congruence and the SAS (side-angle-side) congruence criterion.īy the transitive property of congruence, if AB is congruent to DC and BC is congruent to DA, then ABDC is a parallelogram. Therefore, by the SSS 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 SAS congruence criterion, we can conclude that ΔABC is congruent to ΔCDA. 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). (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. 3 answers The last two steps of the proof are: 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. ![]()
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