Question

u is the midpoint of \\( \overline { s t } \\). complete the proof that \\( \triangle r s u \cong \triangle r t u \\).

Explanation:

Step1: Given

This is the information provided in the problem statement.

Step2: Given

This is the information provided in the problem statement (marked on the diagram).

Step3: Definition of mid - point

Since \(U\) is the mid - point of \(\overline{ST}\), by the definition of a mid - point, \(SU = TU\), so \(\overline{SU}\cong\overline{TU}\).

Step4: Reflexive property of congruence

Any segment is congruent to itself. So, \(\overline{RU}\cong\overline{RU}\).

Step5: SSS (Side - Side - Side) congruence criterion

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Here, \(\overline{RS}\cong\overline{RT}\), \(\overline{SU}\cong\overline{TU}\), and \(\overline{RU}\cong\overline{RU}\), so \(\triangle RSU\cong\triangle RTU\) by SSS.

Answer:

1. Given
2. Given
3. Definition of mid - point
4. Reflexive property of congruence
5. SSS (Side - Side - Side) congruence criterion