The expression used to prove if the triangles are similar is option D:
PQ/DE = 6/9
Let's find if the triangles are similar:
If the two triangles are similar, then the quotient between correspodent sides in both triangles must be equal.
Then we can write:
PQ/PR = DE/DF
Where:
PQ = 4cm
PR = 6cm
DE = 6cm
DF = 9cm
The equation:
PQ/PR = DE/DF
Can be rewritten as:
PQ/DE = PR/DF
Replacing the sides in the right by the correspondent numbers, we get:
PQ/DE = 6/9
Complete question:
"Which choice could be used to prove that the triangles are similar?
PQ/DE = 6/4
PQ/EF = 4/9
PQ/DE = 4/6
PQ/DE = 6/9"