In `Delta ABC, AB= 4cm, AC = 5 cm and BC = 6 cm`. In `Delta PQR, PR = 4 cm, PQ = 5 cm and RQ = 6 cm. Delta ABC` is congruent to

Options

A. `Delta PQR`
B. `Delta RPQ`
C. `Delta PRQ`
D. `Delta QRP`

Answer

To determine which triangle is congruent to triangle ABC, we will analyze the given information step by step.

### Step 1: Identify the sides of triangle ABC
We are given the lengths of the sides of triangle ABC:
- AB = 4 cm
- AC = 5 cm
- BC = 6 cm

### Step 2: Identify the sides of triangle PQR
We are also given the lengths of the sides of triangle PQR:
- PR = 4 cm
- PQ = 5 cm
- RQ = 6 cm

### Step 3: Compare the sides of both triangles
Now, we will compare the corresponding sides of triangle ABC and triangle PQR:
- AB (4 cm) corresponds to PR (4 cm)
- AC (5 cm) corresponds to PQ (5 cm)
- BC (6 cm) corresponds to RQ (6 cm)

### Step 4: Establish congruence
Since all three pairs of corresponding sides are equal, we can conclude that triangle ABC is congruent to triangle PQR by the Side-Side-Side (SSS) congruence criterion.

### Conclusion
Thus, triangle ABC is congruent to triangle PQR.