Question

use the image to answer the question. based on the markings in the diagram, what additional information must be stated in order to prove \\( \triangle abc \cong \triangle dbc \\) by the asa congruence theorem? (1 point) \\( \overline { a b } \cong \overline { b d } \\) \\( \angle a \cong \angle d \\) \\( \overline { a c } \cong \overline { d c } \\) \\( \overline { b c } \cong \overline { b c } \\)

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 the given diagram

In \(\triangle ABC\) and \(\triangle DBC\), we already have \(\angle ACB=\angle DCB\) (given angle) and \(BC = BC\) (common side).

Step3: Determine the required angle

For ASA, we need another pair of angles. The angles \(\angle A\) and \(\angle D\) are the non - included angles with respect to the common side \(BC\). If \(\angle A\cong\angle D\), then by ASA (\(\angle A\cong\angle D\), \(BC = BC\), \(\angle ACB=\angle DCB\)), \(\triangle ABC\cong\triangle DBC\).

Answer:

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