Question

suppose ( ptcong rs ). what information do you need to conclude that ( \triangle ptscong\triangle rst ) using the sss congruence theorem?

enter your answer in the box.

( congoverline{ps} )

Explanation:

Step1: Recall SSS Congruence Theorem

The SSS (Side - Side - Side) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
We are given that \(PT\cong RS\), and the two triangles \(\triangle PTS\) and \(\triangle RST\) share the side \(TS\). So, \(TS\cong TS\) (reflexive property of congruence).

Step2: Determine the missing side

For \(\triangle PTS\) and \(\triangle RST\) to be congruent by SSS, we need the third pair of sides to be congruent.
In \(\triangle PTS\), the sides are \(PT\), \(TS\), \(PS\); in \(\triangle RST\), the sides are \(RS\), \(TS\), \(RT\).
Since \(PT\cong RS\) and \(TS\cong TS\), we need \(RT\cong PS\).

Answer:

\(\overline{RT}\)