which statement best describes triangles uvw and xyz? they are similar and congruent. they are similar, but…

Answer:

They are similar, but not congruent.

Explanation:

Step1: Check angle - angle similarity

In (\triangle UVW), angles are (40^{\circ}, 50^{\circ}), and (180-(40 + 50)=90^{\circ}). In (\triangle XYZ), angles are (32^{\circ}, 48^{\circ}), and (180-(32 + 48)=100^{\circ}). Also, we can check side - side ratios. For (\triangle UVW) with sides (40,50,60) and (\triangle XYZ) with sides (32,40,48). The ratios of corresponding sides are (\frac{40}{32}=\frac{5}{4}), (\frac{50}{40}=\frac{5}{4}), (\frac{60}{48}=\frac{5}{4}). Since the ratios of corresponding sides are equal ((k = \frac{5}{4})), the triangles are similar.

Step2: Check for congruence

For congruence, corresponding sides must be equal. Since (40\neq32), (50\neq40), (60\neq48), the triangles are not congruent.