Question

question 19 of 50
if $\triangle rsu \sim \triangle vst$, then the triangles are similar by:
image of two triangles with vertices labeled r, u, s and v, t, s, and side lengths: rs=7, us=4, st=8, sv=14
\bigcirc the sas similarity theorem.
\bigcirc the sss similarity theorem.
\bigcirc the aa similarity postulate.

Explanation:

Step1: Identify Vertical Angles

∠RSU and ∠VST are vertical angles, so they are equal.

Step2: Check Side Ratios

Calculate ratios of corresponding sides:
$\frac{RS}{VS} = \frac{7}{14} = \frac{1}{2}$,
$\frac{SU}{ST} = \frac{4}{8} = \frac{1}{2}$.
So two sides are proportional, and included angle (vertical angles) is equal.

Step3: Apply SAS Similarity

By SAS (Side - Angle - Side) similarity theorem, if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, triangles are similar.

Answer:

the SAS similarity theorem.