Answer:
D. [tex]\frac{DE}{PQ} = \frac{3}{2}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{DE}{PR}=\frac{FE}{RQ} = \frac{3}{2}[/tex]
SSS Similarity theorem: Triangles are similar if all three sides in one triangle are in the same proportion to the corresponding sides in the other.
Applying SSS theorem to ΔDEF and Δ PQR :
[tex]\frac{DE}{PQ} = \frac{EF}{QR} = \frac{DF}{PR}[/tex]
But
[tex]\frac{DF}{PR} = \frac{EF}{RQ} = \frac{3}{2}[/tex]
Therefore,
[tex]\frac{DE}{PQ} = \frac{3}{2}[/tex]
This is the additional information needed to show the triangles are similar as per SSS similarity theorem.
