Question

for the triangles below, use the tools to move the solid triangle exactly onto the dashed one.
then answer the parts below.
(a) complete the congruence statements below.
(b) complete the congruence statements below.
(c) are all three pairs of corresponding sides and all three pairs of
corresponding angles 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 parts

When moving the solid triangle \( \triangle EFD\) onto the dashed triangle \( \triangle RTS\), we find the corresponding vertices. \(E\) corresponds to \(R\), \(F\) corresponds to \(T\), \(D\) corresponds to \(S\).

Step2: Complete side - congruence statements

For sides:

• \( \overline{ST}\) corresponds to \( \overline{DF}\), so \( \overline{ST}\cong\overline{DF}\)
• \( \overline{TR}\) corresponds to \( \overline{FE}\), so \( \overline{TR}\cong\overline{FE}\)
• \( \overline{RS}\) corresponds to \( \overline{ED}\), so \( \overline{RS}\cong\overline{ED}\)

Step3: Complete angle - congruence statements

For angles:

• \( \angle S\) corresponds to \( \angle D\), so \( \angle S\cong\angle D\)
• \( \angle T\) corresponds to \( \angle F\), so \( \angle T\cong\angle F\)
• \( \angle R\) corresponds to \( \angle E\), so \( \angle R\cong\angle E\)

Step4: Answer part (c)

Since we can move one triangle onto the other (they are congruent), and for congruent triangles, all three pairs of corresponding sides and all three pairs of corresponding angles are congruent.

Answer:

(a) \( \overline{ST}\cong\overline{DF}\), \( \overline{TR}\cong\overline{FE}\), \( \overline{RS}\cong\overline{ED}\)
(b) \( \angle S\cong\angle D\), \( \angle T\cong\angle F\), \( \angle R\cong\angle E\)
(c) Yes, and the triangles are congruent.