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 $angle bcongangle d$ by the reflexive property of congruence $overline{ac}congoverline{ac}$ by the reflexive property of congruence $overline{da}congoverline{bc}$ by the reflexive property of congruence

Explanation:

Step1: Recall ASA Congruence Theorem

ASA (Angle - Side - Angle) requires two pairs of congruent angles and the included side congruent.

Step2: Identify given angles

Given $\angle BCA\cong\angle DAC$ and $\angle BAC\cong\angle DCA$. The included side for these angle - pairs in $\triangle ABC$ and $\triangle CDA$ is $\overline{AC}$.

Step3: Apply reflexive property

By the reflexive property of congruence, any segment is congruent to itself, so $\overline{AC}\cong\overline{AC}$. This is the additional information needed for ASA.

Answer:

C. $\overline{AC}\cong\overline{AC}$ by the Reflexive Property of Congruence