Question

given statement
\\( \overline { r u } \cong \overline { t u } \\)
diagram
yes/no?
is enough information given in the figure to show that the given statement is true?

Explanation:

Step1: Analyze the triangles

We have two triangles \( \triangle RUS\) and \( \triangle TUS\). We know that \( RS = TS\) (from the marks on the diagram), \( \angle RSU=\angle TSU = 90^{\circ}\) (assuming \( US\) is perpendicular as per the right - angle - like appearance in the diagram), and \( US\) is a common side.

Step2: Use the Hypotenuse - Leg (HL) congruence criterion

For right - angled triangles, if the hypotenuse and one leg are equal. In \( \triangle RUS\) and \( \triangle TUS\), \( RU\) and \( TU\) are hypotenuses. By HL congruence, \( \triangle RUS\cong\triangle TUS\). Then, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \( RU = TU\).

Answer:

Yes