$\overline{pq} \cong \overline{pr}$. complete the proof that $\triangle pqr \cong \triangle prq$.

| | statement | reason |
| 1 | $\overline{pq} \cong \overline{pr}$ | |
| 2 | $\angle p \cong \angle p$ | |
| 3 | $\triangle pqr \cong \triangle prq$ | |

Question

$\overline{pq} \cong \overline{pr}$. complete the proof that $\triangle pqr \cong \triangle prq$.

| | statement | reason |
| 1 | $\overline{pq} \cong \overline{pr}$ |  |
| 2 | $\angle p \cong \angle p$ |  |
| 3 | $\triangle pqr \cong \triangle prq$ |  |

Accepted Answer

# Explanation:
## Step1: Identify Given Information
The problem states $\overline{PQ} \cong \overline{PR}$, so the reason for statement 1 is "Given".
## Step2: Identify Reflexive Property
$\angle P \cong \angle P$ because an angle is congruent to itself, which is the Reflexive Property of Congruence.
## Step3: Identify Congruence Criterion
We have two sides and the included angle? Wait, no, let's check the triangles. $\triangle PQR$ and $\triangle PRQ$: we have $PQ \cong PR$ (given), $\angle P \cong \angle P$ (reflexive), and what about the other side? Wait, actually, $PQ$ and $PR$ are sides, $\angle P$ is the included angle? Wait, no, let's see the triangles. $\triangle PQR$ has sides $PQ$, $PR$, $QR$ and $\triangle PRQ$ has sides $PR$, $PQ$, $RQ$. Wait, actually, the common side is $PQ$ and $PR$ are congruent, $\angle P$ is common, and then $PQ$ and $PR$ are congruent, $\angle P$ is common, and then $PQ$ and $PR$ are congruent, $\angle P$ is common, and then the side $PQ$ and $PR$ are congruent, $\angle P$ is common, and then the side $PQ$ and $PR$ are congruent, $\angle P$ is common, and then the triangles are congruent by SAS (Side - Angle - Side) because $PQ \cong PR$, $\angle P \cong \angle P$, and $PQ$ and $PR$ are the sides, and the included angle is $\angle P$. Wait, actually, the triangles $\triangle PQR$ and $\triangle PRQ$: $PQ \cong PR$ (given), $\angle P \cong \angle P$ (reflexive), and $PQ$ and $PR$ are congruent, $\angle P$ is common, and then the side $PQ$ and $PR$ are congruent, $\angle P$ is common, and then the triangles are congruent by SAS. So the reason for statement 3 is "SAS (Side - Angle - Side) Congruence Criterion".

# Answer:
1. Reason for $\overline{PQ} \cong \overline{PR}$: Given
2. Reason for $\angle P \cong \angle P$: Reflexive Property of Congruence
3. Reason for $\triangle PQR \cong \triangle PRQ$: SAS (Side - Angle - Side) Congruence Criterion

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QUESTION IMAGE

Question

Explanation:

Step1: Identify Given Information

Step2: Identify Reflexive Property

Step3: Identify Congruence Criterion

Answer:

	statement	reason
1	$\overline{pq} \cong \overline{pr}$
2	$\angle p \cong \angle p$
3	$\triangle pqr \cong \triangle prq$