Question

Given that DF/PR=FE/RQ=3/2, what additional information is needed to prove △DEF ~ △PQR using the SSS similarity theorem?

A. DE ≅ PQ
B. C. DE/EF = 3/2
D. DE/PQ = 3/2

Answer 1

D

Explanation:

Answer 2

Option D.

Explanation:

Given information:
`(DF)/(PR)=(FE)/(RQ)=(3)/(2)`.

We need to find the additional information which is needed to prove △DEF ~ △PQR using the SSS similarity theorem.

According to the SSS similarity theorem, two triangles are similar if their corresponding sides are proportional.

Using SSS similarity theorem, both △DEF and △PQR are similar if

`(DE)/(PQ)=(E F)/(Q R)=(DF)/(PR)`

If can be written as

`(DE)/(PQ)=(FE)/(RQ)=(DF)/(PR)`

It is given that
`(DF)/(PR)=(FE)/(RQ)=(3)/(2)`.

So, the additional information which is needed to prove △DEF ~ △PQR using the SSS similarity theorem is
`(DE)/(PQ)=(3)/(2)`.

Therefore, the correct option is D.