Question

the proof that △qpt ≅ △qrt is shown. given: $overline{sp}congoverline{sr}$ prove: △qpt ≅ △qrt what is the missing reason in the proof? statements reasons 1. $overline{sp}congoverline{sr}$ 1. given 2. $overline{st}perpoverline{pr}$ 2. converse of the perpendicular bisector theorem 3. $overline{pt}congoverline{rt}$ 3.? 4. $overline{qt}perpoverline{pr}$ 4. st and qt name the same line. 5. $overline{qp}congoverline{qr}$ 5. perpendicular bisector theorem 6. △qpt ≅ △qrt 6. hl theorem definition of perpendicular bisector definition of congruence reflexive property substitution property

Explanation:

Since $\overline{ST}\perp\overline{PR}$ (from step 2) and a perpendicular bisector is a line that is perpendicular to a segment and divides it into two equal - length segments, and we know that a point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Given $\overline{SP}\cong\overline{SR}$, by the definition of a perpendicular bisector, $\overline{ST}$ is the perpendicular bisector of $\overline{PR}$, so $\overline{PT}\cong\overline{RT}$.

Answer:

definition of perpendicular bisector