Question

rowena is proving that \\( \overline { a d } \cong \overline { e b } \\). which statement does the \\( \bullet \\) represent in her proof?
\\( \triangle a c d \cong \triangle e c b \\)
\\( \triangle a c d \cong \triangle e f d \\)
\\( \triangle a f b \cong \triangle e f d \\)
\\( \triangle a f b \cong \triangle e c b \\)

Explanation:

Step1: Recall ASA (Angle - Side - Angle) congruence criterion

ASA 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: Identify the triangles and their parts

We have \(\angle CAD\cong\angle CEB\) (given as statement 2), \(AC = CE\) (from statement 6, since \(AC\cong CE\) by statement 7 which is based on \(AC = CE\) from substitution in step 6), and \(\angle C\cong\angle C\) (reflexive property, statement 8).
The two triangles involved are \(\triangle ACD\) and \(\triangle ECB\).

Answer:

\(\triangle ACD\cong\triangle ECB\)