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.
(images of triangles uvw and xyz with side lengths: uvw has sides 50, 60, 40; xyz has sides 32, 40, 48 and angle markings indicating corresponding angles)

Explanation:

Step1: Check Similarity

To check similarity, we can use the Angle - Angle (AA) criterion. In triangle UVW and triangle XYZ, we can see that the corresponding angles are equal (indicated by the arc marks). So, by AA similarity criterion, the triangles are similar.

Step2: Check Congruence

For congruence, the corresponding sides must be equal in length. Let's check the ratios of the sides.
In triangle UVW, the sides are \( UV = 50\), \( VW=60\), \( UW = 40\)
In triangle XYZ, the sides are \( XY = 40\), \( YZ=48\), \( XZ = 32\)

Let's find the ratios of corresponding sides:
\(\frac{UV}{XY}=\frac{50}{40}=\frac{5}{4}\)
\(\frac{VW}{YZ}=\frac{60}{48}=\frac{5}{4}\)
\(\frac{UW}{XZ}=\frac{40}{32}=\frac{5}{4}\)

The ratios of the corresponding sides are equal (all \(\frac{5}{4}\)), but the lengths of the sides are not equal (e.g., \(50
eq40\), \(60
eq48\), \(40
eq32\)). Congruent triangles require corresponding sides to be equal in length. So, the triangles are similar but not congruent.

Answer:

They are similar, but not congruent.