Question

in the figure shown, what additional information is needed to show that ( \triangle abccong\triangle def ) by sss?

a ( mangle c )
b ( overline{ac}congoverline{df} )
c ( overline{ab}congoverline{de} )
d ( mangle e )

Explanation:

Step1: Recall SSS congruence criterion

SSS (Side - Side - Side) congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze the given sides

In \(\triangle ABC\) and \(\triangle DEF\), assume we already know one pair of sides is congruent (from the markings in the figure). For SSS, we need to check the other pairs of sides.
For \(\triangle ABC\) and \(\triangle DEF\), if \(\overline{AC}\cong\overline{DF}\), along with the other two pairs of congruent sides (implied by the markings in the figure), then by SSS \(\triangle ABC\cong\triangle DEF\).

Answer:

B. \(\overline{AC}\cong\overline{DF}\)