Question

determine if triangle tuv and triangle wxy are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.) answer the triangles similar.

Explanation:

Step1: Find angles in △TUV

In △TUV, ∠T = 30°, ∠U = 90°, so ∠V = 180° - 30° - 90° = 60°.

Step2: Find angles in △WXY

In △WXY, ∠W = 30°, ∠Y = 60°, so ∠X = 180° - 30° - 60° = 90°.

Step3: Compare angles

∠T = ∠W = 30°, ∠V = ∠Y = 60°, ∠U = ∠X = 90°. By AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. So △TUV ~ △WXY by AA similarity.

Answer:

The triangles are similar. We know this because two angles of triangle \( TUV \) ( \( 30^\circ \) and \( 90^\circ \) or \( 30^\circ \) and \( 60^\circ \)) are equal to two angles of triangle \( WXY \) ( \( 30^\circ \) and \( 60^\circ \) or \( 30^\circ \) and \( 90^\circ \)) respectively, satisfying the AA (Angle - Angle) similarity criterion.