Question

(a) complete the congruence statements below.

\\( \angle g \cong \\) (choose one)

\\( \angle f \cong \\) (choose one)

\\( \angle e \cong \\) (choose one)

(b) complete the congruence statements below.

\\( \overline { g f } \cong \\) (choose one)

\\( \overline { f e } \cong \\) (choose one)

\\( \overline { e g } \cong \\) (choose one)

(c) are all three pairs of corresponding angles and all three pairs of corresponding sides congruent?

no, and the triangles are not congruent.

no, and the triangles are congruent.

yes, and the triangles are not congruent.

yes, and the triangles are congruent.

Explanation:

Step1: Identify corresponding angles

In congruent triangles, corresponding angles are equal. By observing the triangles, we can match the angles.

• $\angle G$ corresponds to $\angle J$
• $\angle F$ corresponds to $\angle K$
• $\angle E$ corresponds to $\angle L$

Step2: Identify corresponding sides

In congruent triangles, corresponding sides are equal.

• $\overline{GF}$ corresponds to $\overline{JK}$
• $\overline{FE}$ corresponds to $\overline{KL}$
• $\overline{EG}$ corresponds to $\overline{LJ}$

Step3: Determine congruence

If all three pairs of corresponding angles and all three pairs of corresponding sides are congruent, then the triangles are congruent.

Answer:

(a) $\angle G\cong\angle J$, $\angle F\cong\angle K$, $\angle E\cong\angle L$
(b) $\overline{GF}\cong\overline{JK}$, $\overline{FE}\cong\overline{KL}$, $\overline{EG}\cong\overline{LJ}$
(c) Yes, and the triangles are congruent.