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SR is a perpendicular bisector of APSZ.

Based on the definition of a perpendicular bisector, which of the following must be true?
*Select all that apply.
OPR RZ
OZPSR ZSPR
Om/SRZ = 90°
OPS PR
OZSZR 2ZZSR

1 Answer

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SR, being a perpendicular bisector of APSZ, divides the segment into two equal parts. This implies that OP is equal to RO and OZ is equal to RZ, as O and P, as well as O and Z, are equidistant from the midpoint of APSZ.

The perpendicular nature of SR to APSZ establishes a right angle at ∠SRZ, making ∆SRZ a right-angled triangle with m/∠SRZ = 90°. The concept of bisector symmetry extends to angles, with angles OPS and PRO being congruent, as well as angles SZR and ZZR.

The perpendicular bisector property contributes to the overall congruence and equality in the triangle and segments formed by APSZ. Thus, the given statements OP=RO, OZ=RZ, and ∠m/SRZ = 90°, along with the congruence of angles OPS/PRO and SZR/ZZR, align with the definition of a perpendicular bisector.

SR is a perpendicular bisector of APSZ. Based on the definition of a perpendicular-example-1
User Stefan Schultze
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