Question

which statement is true?
△rst is similar to △utv.
△rst is not similar to △utv.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find angles in \(\triangle RST\)

In \(\triangle RST\), \(\angle S = 90^{\circ}\), \(\angle R=39^{\circ}\). Using the angle - sum property of a triangle (\(\angle S+\angle R+\angle STR = 180^{\circ}\)), we get \(\angle STR=180^{\circ}-(90^{\circ} + 39^{\circ})=51^{\circ}\).

Step2: Find angles in \(\triangle UTV\)

In \(\triangle UTV\), using the angle - sum property (\(\angle U+\angle V+\angle TUV = 180^{\circ}\)), assume \(\angle TUV = 90^{\circ}\) (right - angled at \(T\) as per the parallel lines and transversal concept, since \(SR\parallel TV\) and \(ST\) is a transversal). Given \(\angle V = 61^{\circ}\), then \(\angle U=180^{\circ}-(90^{\circ}+61^{\circ}) = 29^{\circ}\).
Since the angles of \(\triangle RST\) (\(90^{\circ},39^{\circ},51^{\circ}\)) and \(\triangle UTV\) (\(90^{\circ},29^{\circ},61^{\circ}\)) are not equal, the triangles are not similar.

Answer:

\(\triangle RST\) is not similar to \(\triangle UTV\)