What is the missing reason in the proof? Statements Reasons 1. line segment SP is congruent to line segment SR 1. given 2. line segment ST perpendicular to line segment PR 2. converse of the perpendicular bisector theorem 3. line segment PT is congruent to line segment RT 3. ? 4. line segment QT perpendicular to line segment PR 4. line segment ST and line segment QT name the same line. 5. line segment QP is congruent to line segment QR 5. perpendicular bisector theorem 6. triangle QPT is congruent to triangle QRT 6. HL theorem
Answer
A
definition of congruence
B
reflexive property
C
definition of perpendicular bisector
D
substitution property
Explanation
The converse of the perpendicular bisector theorem shows that the line through S and T is the perpendicular bisector of PR. By the definition of a perpendicular bisector, it meets PR at its midpoint T, so PT is congruent to RT. The missing reason is “definition of perpendicular bisector.”
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