Question

Construct a line segment AB of length 5cm, draw its perpendicular bisector at point M.
take any point P on the perpendicular bisector, join PA and PB, the relation between PA and PB is?

• A. $PA>PB$
• B. $PA=PB$
• C. $PA<PB$
• D. $PA$ and $PB$ are parallel

Answer 1

Answer: (B)

$PA=PB$

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of the original line segment.

Take any point on the perpendicular bisector and join it with the ends of the line segment considered. Then the line segments thus formed are equal.

Consider the figure,

$AB$ is the base, $MP$ is the perpendicular bisector to $AB$

Join $PA$ and $BP$

In triangles $AMP$ and $PMB$

$AM=MB$

$\angle AMP=\angle PMB={90}^{\circ }$

$PM$ is the common side

From $SAS$ postulate, the triangles are congruent. Hence, the third sides are also equal.

i.e., $AP=BP$