Question

δtux and δtvw are shown below. which statement is true? δtux is similar to δtvw. δtux is not similar to δtvw. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Check for common angles

Both \(\triangle TUX\) and \(\triangle TVW\) share the angle \(\angle T\).

Step2: Check for right angles

\(\angle TUX = 90^{\circ}\) and \(\angle TVW=90^{\circ}\) (given by the right - angle symbols).

Step3: Apply AA (Angle - Angle) similarity criterion

Since two angles of \(\triangle TUX\) are equal to two angles of \(\triangle TVW\) ( \(\angle T\) is common and \(\angle TUX=\angle TVW = 90^{\circ}\)), by the AA similarity criterion, the two triangles are similar.

Answer:

\(\triangle TUX\) is similar to \(\triangle TVW\).