Question

are these scalene triangles similar?

(image of two triangles with vertices v, w, s and u, w, t, with side lengths: vw = 42, ws = 48, wt = 56, wu = 64)

options: yes (selected), no

write a similarity statement.
△ ~ △

Explanation:

Step1: Check Proportions of Sides

First, identify the sides around the vertical angles (which are equal). For triangles \( \triangle VWS \) and \( \triangle TWU \), the sides are \( VW = 42 \), \( WS = 48 \), \( WT = 56 \), \( WU = 64 \). Calculate the ratios: \( \frac{VW}{WT}=\frac{42}{56}=\frac{3}{4} \), \( \frac{WS}{WU}=\frac{48}{64}=\frac{3}{4} \). Since the included angles (vertical angles) are equal, by SAS similarity, the triangles are similar.

Step2: Determine Similarity Statement

Match the corresponding sides. \( VW \) corresponds to \( WT \), \( WS \) corresponds to \( WU \), so \( \triangle VWS \sim \triangle TWU \).

Answer:

\(\triangle VWS \sim \triangle TWU\)