Question

the proof that δqpt ≅ δqrt is shown. given: sp ≅ sr prove: δqpt ≅ δqrt what is the missing reason in the proof? statements reasons 1. sp ≅ sr 1. given 2. st ⊥ pr 2. converse of the perpendicular bisector theorem 3. pt ≅ rt 3. ? 4. qt ⊥ pr 4. st and qt name the same line. 5. qp ≅ qr 5. perpendicular bisector theorem 6. δqpt ≅ δqrt 6. hl theorem definition of perpendicular bisector definition of congruence reflexive property substitution property

Explanation:

• The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. The converse of the perpendicular bisector theorem is used in step 2 to establish that \(ST\perp PR\).
• The definition of a perpendicular bisector is that a perpendicular bisector of a segment divides the segment into two congruent parts. Since \(ST\perp PR\) (from step 2), by the definition of a perpendicular bisector, \(PT\cong RT\).

Answer:

definition of perpendicular bisector