Question

determine if triangle uvw and triangle xyz are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Find the third angle of triangle \( XYZ \)

The sum of angles in a triangle is \( 180^{\circ} \). For \( \triangle XYZ \), if \( \angle X = 49^{\circ} \) and \( \angle Y=82^{\circ} \), then \( \angle Z=180^{\circ}-(49^{\circ} + 82^{\circ})=49^{\circ} \).

Step2: Check the ratios of the corresponding sides

For \( \triangle UVW \) and \( \triangle XYZ \), we have the following ratios of corresponding sides:
\(\frac{UV}{XZ}=\frac{11}{56}\), \(\frac{UW}{XY}=\frac{14}{44}=\frac{7}{22}\). Since \(\frac{11}{56}
eq\frac{7}{22}\) (cross - multiply: \(11\times22 = 242\) and \(56\times7=392\), \(242
eq392\)).

Answer:

Triangle \( UVW \) and triangle \( XYZ \) are not similar.