11. If $$ riangle M N O \cong riangle P Q R $$, which of the following can you $$ N O T $$ conclude as being true? $$ \overline{\mathrm{NO}} \cong \overline{\mathrm{QR}} $$ $$ \overline{M N} \cong \overline{P R} $$ $$ \angle \mathrm{~N} \cong \angle \mathrm{Q} $$

Question

11. If $$ 	riangle M N O \cong 	riangle P Q R $$, which of the following can you $$ N O T $$ conclude as being true? $$ \overline{\mathrm{NO}} \cong \overline{\mathrm{QR}} $$ $$ \overline{M N} \cong \overline{P R} $$ $$ \angle \mathrm{~N} \cong \angle \mathrm{Q} $$

UpStudy AI · Accepted Answer

To determine which statement cannot be concluded as true from the given congruent triangles $$ 	riangle MNO \cong 	riangle PQR $$, let's analyze the correspondence between the sides and angles of the triangles.

**Given:**
- $$ 	riangle MNO \cong 	riangle PQR $$

**Correspondence:**
- $$ M $$ corresponds to $$ P $$
- $$ N $$ corresponds to $$ Q $$
- $$ O $$ corresponds to $$ R $$

**Implications of Congruence:**
1. **Sides:**
   - $$ \overline{MN} \cong \overline{PQ} $$
   - $$ \overline{NO} \cong \overline{QR} $$
   - $$ \overline{OM} \cong \overline{RP} $$

2. **Angles:**
   - $$ \angle M \cong \angle P $$
   - $$ \angle N \cong \angle Q $$
   - $$ \angle O \cong \angle R $$

**Evaluating the Statements:**

1. **$$ \overline{NO} \cong \overline{QR} $$**
   - **True.** This directly follows from the congruence $$ 	riangle MNO \cong 	riangle PQR $$.

2. **$$ \overline{MN} \cong \overline{PR} $$**
   - **False.** According to the correspondence:
     - $$ \overline{MN} \cong \overline{PQ} $$, not $$ \overline{PR} $$.

3. **$$ \angle N \cong \angle Q $$**
   - **True.** This is a direct consequence of the congruent triangles.

**Conclusion:**
The statement **$$ \overline{MN} \cong \overline{PR} $$** cannot be concluded as true based on the given information.

**Answer:**  
$$ \overline{M N} \cong \overline{P R} $$ cannot be concluded as being true.
$$ \overline{M N} \cong \overline{P R} $$ cannot be concluded as being true.

11. If \( \triangle M N O \cong \triangle P Q R \), which of the following can you \( N O T \) conclude as being true? \( \overline{\mathrm{NO}} \cong \overline{\mathrm{QR}} \) \( \overline{M N} \cong \overline{P R} \) \( \angle \mathrm{~N} \cong \angle \mathrm{Q} \)

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