Question

in the figure shown, what additional information is needed to show that <script>\triangle abc\cong\triangle def</script> by asa?
a ( m\angle c )
b ( \overline{ab}\cong\overline{de} )
c ( m\angle f )
d ( \overline{bc}\cong\overline{ef} )

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: Analyze the given angles and sides

In \(\triangle ABC\) and \(\triangle DEF\), we already have two angles: \(\angle B\cong\angle E\) and \(\angle A\cong\angle D\). For ASA, we need the included side. The included side between \(\angle A\) and \(\angle B\) in \(\triangle ABC\) is \(AB\), and the included side between \(\angle D\) and \(\angle E\) in \(\triangle DEF\) is \(DE\).

Answer:

B. \(\overline{AB}\cong\overline{DE}\)