Question

Are the two triangles similar? How do you know? (What Theorem?)

Answer 1

Yes they are similar by SAS or side-angle-side Similarity Theorem

Explanation:

Given

In Triangle UWV

WU=6

VU=4

In Triangle UST

US=9

UT=6

Solution

AngleWUV = AngleSUT as they are Vertically Opposite Angles

And

US/UW = UT/UV

or

9/6 = 6/4

which can be simplified into

3/2 = 3/2

Since the ratio of two sides and an angle is equal, TriangleUWV is similar to TriangleUST by Side-Angle-Side Similarity Theorem