Question

r is the midpoint of \\( \overline{qs} \\), \\( \overline{ru} \cong \overline{qt} \\), and \\( \overline{su} \cong \overline{rt} \\). complete the proof that \\( \delta rsu \cong \delta qrt \\).
statement
1 r is the midpoint of \\( \overline{qs} \\)
2 \\( \overline{ru} \cong \overline{qt} \\)
3 \\( \overline{su} \cong \overline{rt} \\)
4 \\( \overline{qr} \cong \overline{rs} \\)
5
reason
given
given
given
definition of midpoint

Explanation:

Step1: Use SSS Congruence Criterion

Since we have \( \overline{RU}\cong\overline{QT}\), \( \overline{SU}\cong\overline{RT}\), and \( \overline{QR}\cong\overline{RS}\) (from the definition of mid - point), by the Side - Side - Side (SSS) congruence criterion for triangles.
The SSS criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
For \( \triangle RSU\) and \( \triangle QRT\), we have:

• \( \overline{SU}\cong\overline{RT}\) (given)
• \( \overline{RU}\cong\overline{QT}\) (given)
• \( \overline{RS}\cong\overline{QR}\) (definition of mid - point)

Answer:

\(\triangle RSU\cong\triangle QRT\) (by SSS congruence criterion)