Question

which statement best describes triangles uvw and xyz?
○ they are similar and congruent.
○ they are similar, but not congruent.
○ they are congruent, but not similar.
○ they are neither congruent nor similar.
(image shows triangle uvw with sides 50, 60, 40 and triangle xyz with sides 32, 40, 48, with angle markings indicating congruent angles.)

Explanation:

Step1: Check similarity (AA criterion)

Triangles \( UVW \) and \( XYZ \): Angles with the same markings are equal. So, two angles in \( \triangle UVW \) equal two angles in \( \triangle XYZ \), so they are similar (AA similarity).

Step2: Check congruence (side lengths)

Sides of \( \triangle UVW \): \( 40, 50, 60 \). Sides of \( \triangle XYZ \): \( 32, 40, 48 \). Ratios: \( \frac{32}{40} = 0.8 \), \( \frac{40}{50} = 0.8 \), \( \frac{48}{60} = 0.8 \). So sides are proportional (scale factor \( 0.8 \)), not equal. Thus, not congruent.

Answer:

They are similar, but not congruent.