In given figure AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B
Open in App
Solution
Verified by Toppr
Given AB is a line segment and l is perpendicular bisector. if point p lies on l.
Join P to A and B
The perpendicular l passe through line AB, cut on C
Then C is the midpoint of AB
Then AC=BC
In ΔPCA And ΔPCB
AC=BC (Given M is the Midpoint of AB)
∠PCA=∠PCB=900 (l is the perpendicular on AB)
PC=PC
∴ΔPCA≅ΔPCB
∴PA=PB[henceproved]
Was this answer helpful?
8
Similar Questions
Q1
In given figure AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B
View Solution
Q2
AB is a line segment and line l is its perpendicular bisector.If a point P lies on l, Show that P is equidistant from A and B
View Solution
Q3
AB is a line segment and line l is its perpendicular bisector. Show that every point on line l is equidistant from A and B.
View Solution
Q4
In given figure AB is a line-segment. P and Q are points on either side of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the perpendicular bisector of AB
View Solution
Q5
AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Figure). Show that the line PQ is perpendicular bisector of AB.