Question

given statement ( overline{ru}congoverline{tu} ) diagram yes/no? is enough information given in the figure to show that the given statement is true?

Explanation:

Step1: Check the congruence conditions

To prove $\overline{RU}\cong\overline{TU}$, we need to check if there is a congruence of triangles. However, from the given diagram, we only know that $RS = ST$ (marked as equal segments) and $\angle RSC=\angle TSC = 90^{\circ}$ (assuming $CS$ is a perpendicular bisector - but not given), and $\angle RCS=\angle TCS$ (given as an angle). But we don't have enough information to prove that $\triangle RCS\cong\triangle TCS$ (we lack a side - side - side (SSS), side - angle - side (SAS), angle - side - angle (ASA) or hypotenuse - leg (HL) for right triangles). Without triangle congruence, we can't directly say $RU = TU$.

Answer:

No