Question

unit 5 triangle congruence > lesson 5 the asa congruence theorem back to intro page based on the markings in the diagram, what additional information must be stated in order to prove △abc≅△dbc by the asa congruence theorem? (1 point) o $overline{ac}congoverline{dc}$ o $overline{ab}congoverline{bd}$ o $angle acongangle d$ o $overline{bc}congoverline{bc}$

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. In \(\triangle ABC\) and \(\triangle DBC\), side \(BC\) is common (reflexive property, \(\overline{BC}\cong\overline{BC}\)).

Step2: Analyze given options

We already have the common side \(BC\). We need two pairs of congruent angles. If \(\angle A\cong\angle D\), along with the common side \(BC\) and the vertical - angles (which are congruent), we can use ASA. The other options about side - congruence (\(\overline{AC}\cong\overline{DC}\), \(\overline{AB}\cong\overline{BD}\)) are not relevant for ASA, and \(\overline{BC}\cong\overline{BC}\) is already a given reflexive property.

Answer:

\(\angle A\cong\angle D\)