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.)

triangle uvw: sides are 14 (wu), 14 (uv), 18 (vw)
triangle xyz: sides are 56 (zx), 56 (xy), 72 (zy)

answer
attempt 1 out of 2
the triangles dropdown similar.

Explanation:

Step1: List side lengths of both triangles

Triangle UVW: $UW=14$, $UV=14$, $VW=18$
Triangle XYZ: $XY=56$, $ZX=56$, $ZY=72$

Step2: Calculate side length ratios

$\frac{UW}{XY} = \frac{14}{56} = \frac{1}{4}$
$\frac{UV}{ZX} = \frac{14}{56} = \frac{1}{4}$
$\frac{VW}{ZY} = \frac{18}{72} = \frac{1}{4}$

Step3: Compare ratios for similarity

All corresponding side ratios are equal.

Answer:

The triangles are similar. They are similar by the Side-Side-Side (SSS) Similarity Criterion, as all pairs of corresponding sides have an equal ratio of $\frac{1}{4}$.