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) $overline{ab}congoverline{cd}$ by the triangle angle sum theorem. $overline{da}congoverline{bc}$ by the reflexive property of congruence. $angle bcongangle d$ by the reflexive property of congruence. $overline{ac}congoverline{ac}$ by the reflexive property of congruence

Explanation:

Step1: Recall ASA Congruence Theorem

The ASA (Angle - Side - Angle) Congruence Theorem 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. In \(\triangle ABC\) and \(\triangle CDA\), we already have \(\angle BCA\cong\angle DAC\) and \(\angle BAC\cong\angle DCA\). The included side for these pairs of angles is \(AC\) for both triangles.

Step2: Apply reflexive property

The reflexive property of congruence states that any segment is congruent to itself. So, we need to state that \(\overline{AC}\cong\overline{AC}\) by the reflexive property of congruence.

Answer:

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