If in two `DeltaABC` and `DeltaPQR`, `(AB)/(QR)=(BC)/(PR)=(CA)/(PQ)`, then

Options

A. `DeltaPQR~DeltaCAB`
B. `DeltaPQR~DeltaABC`
C. `DeltaCBA~DeltaPQR`
D. `DeltaBCA~DeltaPQR`

Explanation

To solve the problem, we need to show that the triangles ABC and PQR are similar based on the given ratios of their corresponding sides.

### Step-by-Step Solution:

1. **Understanding the Given Ratios**:
We are given that:
\[ \frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ} \]
This means that the ratios of the lengths of the corresponding sides of triangles ABC and PQR are equal.

**Hint**: Look for the relationship between the sides of the triangles to establish a similarity condition.

2. **Identifying Corresponding Sides**:
From the ratios, we can identify:
- Side AB corresponds to side QR
- Side BC corresponds to side PR
- Side CA corresponds to side PQ

**Hint**: Make sure to match each side of triangle ABC with the correct side of triangle PQR.

3. **Using the Side-Angle-Side (SAS) Similarity Criterion**:
Since the ratios of the corresponding sides are equal, we can apply the Side-Side-Side (SSS) similarity criterion. According to this criterion, if the ratios of the lengths of the corresponding sides of two triangles are equal, then the triangles are similar.

**Hint**: Remember that for triangles to be similar, the corresponding angles must also be equal.

4. **Concluding Similarity**:
Therefore, we conclude that:
\[ \Delta ABC \sim \Delta PQR \]
This means triangle ABC is similar to triangle PQR.

**Hint**: Write down the similarity statement clearly to avoid confusion.

5. **Identifying Other Corresponding Triangles**:
Based on the similarity established, we can also state:
- Triangle BCA is similar to triangle RQP
- Triangle CAB is similar to triangle PQR

**Hint**: Similarity can be transitive; if one triangle is similar to another, you can find other similar pairs.

### Final Answer:
Thus, we can conclude that triangles ABC and PQR are similar, and the correct option is that triangle ABC is similar to triangle PQR.