Question

question 5 of 10
what else would need to be congruent to show that △abc≅△
def by sas?
given:
\\(\overline{ac} \cong \overline{df}\\)
\\(\angle c \cong \angle f\\)
a. \\(\overline{ac} \cong \overline{df}\\)

b. \\(\angle c \cong \angle f\\)

c. \\(\angle a \cong \angle d\\)

d. \\(\overline{bc} \cong \overline{ef}\\)

Explanation:

Step1: Recall SAS Congruence

SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Step2: Analyze Given Information

We are given that $\overline{AC}\cong\overline{DF}$ and $\angle C\cong\angle F$. For SAS, we need two sides and the included angle. The included angle between $\overline{AC}$ and $\overline{BC}$ in $\triangle ABC$ and between $\overline{DF}$ and $\overline{EF}$ in $\triangle DEF$. So we need $\overline{BC}\cong\overline{EF}$ to satisfy SAS (since we already have one side $\overline{AC}\cong\overline{DF}$ and the included angle $\angle C\cong\angle F$, the other side should be $\overline{BC}\cong\overline{EF}$).

Step3: Evaluate Options

• Option A: $\overline{AC}\cong\overline{DF}$ is already given, not what we need.
• Option B: $\angle C\cong\angle F$ is already given, not what we need.
• Option C: $\angle A\cong\angle D$ is not related to SAS with the given information.
• Option D: $\overline{BC}\cong\overline{EF}$ is the side we need for SAS as explained.

Answer:

D. $\overline{BC}\cong\overline{EF}$