Question

the proof that ( \triangle qptcong\triangle qrt ) is shown.
given: ( spcong sr )
prove: ( \triangle qptcong\triangle qrt )
what is the missing reason in the proof?

statements	reasons
2. ( stperp pr )	2. converse of the perpendicular bisector theorem
3. ( ptcong rt )	3. ?
4. ( qtperp pr )	4. st and qt name the same line.
5. ( qpcong qr )	5. perpendicular bisector theorem
6. ( \triangle qptcong\triangle qrt )	6. hl theorem

• definition of perpendicular bisector
• definition of congruence
• reflexive property
• substitution property

Explanation:

The converse of the perpendicular bisector theorem states that if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment. Since \(ST\perp PR\) (from statement 2) and \(SP\cong SR\) (given), by the definition of a perpendicular bisector (a line that is perpendicular to a segment and divides it into two equal parts), \(T\) is the mid - point of \(PR\). So, \(PT\cong RT\) because of the definition of a perpendicular bisector.

Answer:

definition of perpendicular bisector