Question

prove: △prs≅△pts
statement

1. s is the mid - point of (overline{rt})
2. (overline{pr}congoverline{pt})
3. (overline{rs}congoverline{ts})
4. (overline{ps}congoverline{ps})
5. △prs≅△pts

reason

1. given
2. given

3.
4.
5.

Explanation:

Step1: Define mid - point property

Since S is the mid - point of $\overline{RT}$, by the definition of a mid - point, it divides the line segment into two equal parts. So, $\overline{RS}\cong\overline{TS}$.

Step2: Identify reflexive property

$\overline{PS}\cong\overline{PS}$ because any line segment is congruent to itself by the reflexive property of congruence.

Step3: Apply SSS congruence criterion

We have $\overline{PR}\cong\overline{PT}$ (given), $\overline{RS}\cong\overline{TS}$ (from mid - point property) and $\overline{PS}\cong\overline{PS}$ (reflexive property). By the Side - Side - Side (SSS) congruence criterion for triangles, $\triangle PRS\cong\triangle PTS$.

Answer:

1. Reason: Definition of mid - point
2. Reason: Reflexive property of congruence
3. Reason: SSS (Side - Side - Side) congruence criterion