Question

question 5 of 10
what else would need to be congruent to show that $\triangle efg \cong \triangle hij$ by sss?

given:
$\overline{ef} \cong \overline{hi}$
$\overline{fg} \cong \overline{ij}$

a. $\angle f \cong \angle i$
b. $\overline{fg} \cong \overline{hi}$
c. $\overline{ef} \cong \overline{hj}$
d. $\overline{eg} \cong \overline{hj}$

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 two triangles are congruent.

Step2: Identify Given and Needed Sides

For $\triangle EFG$ and $\triangle HIJ$, we are given that $\overline{EF}\cong\overline{HI}$ and $\overline{FG}\cong\overline{IJ}$. We need the third pair of corresponding sides to be congruent. The third sides of $\triangle EFG$ and $\triangle HIJ$ are $\overline{EG}$ and $\overline{HJ}$ respectively. So we need $\overline{EG}\cong\overline{HJ}$.

Let's analyze the other options:

• Option A: $\angle F\cong\angle I$ is an angle - related condition, not for SSS.
• Option B: $\overline{FG}\cong\overline{HI}$ is not a pair of corresponding sides (from the triangle labels, the sides should correspond as $EF - HI$, $FG - IJ$, $EG - HJ$).
• Option C: $\overline{EF}\cong\overline{HJ}$ is not a pair of corresponding sides.

Answer:

D. $\overline{EG}\cong\overline{HJ}$