Question

in the figure shown, what additional information is needed to show that △ abc ≅ △ def by sss? a. m∠c b. \\(\overline{ac} \cong \overline{df}\\) c. \\(\overline{ab} \cong \overline{de}\\) d. m∠e

Explanation:

Step1: Recall SSS Congruence

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

Step2: Analyze Given Congruent Sides

From the figure, we can see that \(BC\cong EF\) (marked with one tick) and \(AB\cong DE\) (marked with two ticks). For SSS, we need the third pair of sides to be congruent. The third sides are \(AC\) (in \(\triangle ABC\)) and \(DF\) (in \(\triangle DEF\)). So we need \(\overline{AC}\cong\overline{DF}\).

Step3: Eliminate Other Options

• Option A: \(m\angle C\) is an angle measurement, SSS does not involve angles, so this is incorrect.
• Option C: \(\overline{AB}\cong\overline{DE}\) is already given (from the markings), so this is not additional information.
• Option D: \(m\angle E\) is an angle measurement, SSS does not involve angles, so this is incorrect.

Answer:

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