Question

Study the figure. (a) Is AR = RP? (b) Does XY bisect BA? (c) Identify two line segments for which XY is the perpendicular bisector? (d)Are these true? (i) AR> RP (ii) AP = PQ (iii) BQ < RP

Answer 1

Given : Perpendicular bisector of AB , AP and BP

To  Find : (a) Is AR = RP? (b) Does XY bisect BA? (c) Identify two line segments for which XY is the perpendicular bisector? (d)Are these true? (i) AR> RP (ii) AP = PQ (iii) BQ < RP

Solution:

 XY is perpendicular bisector of AB intersecting AB at P

=> AP = PB

ST is perpendicular bisector of AP intersecting AP at R

=> AR = RP

DE is perpendicular bisector of PB intersecting BP at Q

=> PQ = QB

=> AR = RP = PQ = AB

AR = RP   YES

XY bisects AB => XY bisect BA   YES

two line segments for which XY is the perpendicular bisector

AP = PB   and  RP = PQ

Hence two line segments are AB  and  RQ

AR> RP  FALSE as AR = RP

AP = PQ   FALSE as  AP = 2 PQ

BQ < RP  FALSE as  BQ = RP

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