Answer:
A reflection, followed by a dilation will map one triangle onto the other, thus proving that the triangles are similar (see the explanation)
Step-by-step explanation:
we know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another
The coordinates of the vertices are:
Q(-6,2), R(-2,6), S(-2,2), and T(-2,0), U(-4,2)
step 1
Plot the triangles to better understand the problem
using a graphing tool
see the attached figure
step 2
Applying a reflection across the line y=2
The new coordinates of triangle UTS would be
U(-4,2)
,T'(-2,4), S(-2,2)
Note: The coordinates of point U and S are the same, because both points are on the reflection line
step 3
Applying a dilation of triangle UT'S by a scale factor of 2 about the point S
The new coordinates of triangle UT'S would be
Q(-6,2), R(-2,6), S(-2,2)
therefore
A reflection, followed by a dilation will map one triangle onto the other, thus proving that the triangles are similar
