Question

which rule explains why these triangles are similar?
v u t
94° 30°
s
30°
94°
w r
sss
sas
aa
none of the above; the triangles cannot be proven similar
write a similarity statement.
△ ~ △

Explanation:

Step1: Identify corresponding angles

In \(\triangle VWU\), angles are \(30^{\circ}\) and \(94^{\circ}\). In \(\triangle TRS\), angles are \(30^{\circ}\) and \(94^{\circ}\).

Step2: Apply AA (Angle - Angle) similarity criterion

Since two pairs of corresponding angles (\(\angle W=\angle T = 30^{\circ}\) and \(\angle U=\angle R=94^{\circ}\)) are equal, by AA similarity criterion, the triangles are similar.

Step3: Write similarity statement

Corresponding angles: \(\angle V\) corresponds to \(\angle S\) (because third angle in \(\triangle VWU\): \(180-(30 + 94)=56^{\circ}\), third angle in \(\triangle TRS\): \(180-(30 + 94)=56^{\circ}\)), \(\angle W\) corresponds to \(\angle T\), \(\angle U\) corresponds to \(\angle R\). So similarity statement is \(\triangle VWU\sim\triangle TRS\)

Answer:

\(\triangle VWU\sim\triangle TRS\)