Question

in parallelogram (abcd), diagonal (overline{ac}) is drawn, and (angle bcacongangle dac) and (angle baccongangle dca). in order to prove (\triangle abccong\triangle cda) by the asa congruence theorem, what additional information must be stated and justified? (1 point) (overline{da}congoverline{bc}) by the reflexive property of congruence. (overline{ac}congoverline{ac}) by the reflexive property of congruence. (angle bcongangle d) by the reflexive property of congruence. (overline{ab}congoverline{cd}) by the triangle angle sum theorem.

Explanation:

Step1: Recall ASA Congruence Theorem

ASA (Angle - Side - Angle) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze given angles and sides

We are given \(\angle BCA\cong\angle DAC\) and \(\angle BAC\cong\angle DCA\). The included side for these angles in \(\triangle ABC\) and \(\triangle CDA\) is \(\overline{AC}\). By the Reflexive Property of Congruence, \(\overline{AC}\cong\overline{AC}\) (a segment is congruent to itself).

Answer:

\(\overline{AC}\cong\overline{AC}\) by the Reflexive Property of Congruence.