State giving reasons, whether the following pairs of triangles are congruent or not: `DeltaDEF` in which `angleE=48^(@), DE=6 cm, EF =8 cm` and `DeltaMNR` in which `angleR=48^(@),MN=6cm,MR=8cm`

Answer

To determine whether the triangles \( \Delta DEF \) and \( \Delta MNR \) are congruent, we will analyze the given information step by step.

### Step 1: Identify the given information for both triangles.
- For \( \Delta DEF \):
- \( \angle E = 48^\circ \)
- \( DE = 6 \, \text{cm} \)
- \( EF = 8 \, \text{cm} \)

- For \( \Delta MNR \):
- \( \angle R = 48^\circ \)
- \( MN = 6 \, \text{cm} \)
- \( MR = 8 \, \text{cm} \)

### Step 2: Compare the angles and sides of both triangles.
- Both triangles have one angle equal to \( 48^\circ \):
- \( \angle E \) in \( \Delta DEF \) and \( \angle R \) in \( \Delta MNR \).

- Both triangles have two sides of equal length:
- \( DE = 6 \, \text{cm} \) and \( MN = 6 \, \text{cm} \)
- \( EF = 8 \, \text{cm} \) and \( MR = 8 \, \text{cm} \)

### Step 3: Check the congruency criteria.
To establish congruency, we can use the Angle-Side-Side (ASS) criterion, but this criterion does not guarantee congruency because the angle is not between the two sides.

- In \( \Delta DEF \), the angle \( E \) is not between the sides \( DE \) and \( EF \).
- In \( \Delta MNR \), the angle \( R \) is not between the sides \( MN \) and \( MR \).

### Step 4: Conclusion.
Since the angle \( E \) in \( \Delta DEF \) is not between the sides \( DE \) and \( EF \), and similarly for \( \Delta MNR \), we cannot conclude that the triangles are congruent based on the information provided.

Thus, \( \Delta DEF \) is **not congruent** to \( \Delta MNR \).

### Final Answer:
The triangles \( \Delta DEF \) and \( \Delta MNR \) are not congruent.

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