Study the diagram. The line $ l $ is perpendicular to line $ m $

(a) $ \mathrm{Is} \mathrm{CE}=\mathrm{EG} $ ?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) $ \mathrm{AC}>\mathrm{FG} $
(ii) $ \mathrm{CD}=\mathrm{GH} $
(iii) $ \mathrm{BC}"

To do:

We have to study the diagram and answer the given questions.

 Solution:

The line \( l \) is perpendicular to line \( m \).

From the figure,

(a) $CE = 2$ units and $EG = 2$ units

This implies,

$\mathrm{CE}=\mathrm{EG}$

(b) $CE = 2$ units, $EG = 2$ units

This implies,

PE bisects CG.

(c) $DE=EF=1$ unit and $PE$ is perpendicular to $DF$

$CE=EG=2$ units and $PE$ is perpendicular to $CG$

This implies,

PE is the perpendicular bisector of line segments DF and CG. 

(d) (i) $AC = 2$ units and $FG = 1$ unit

This implies,

$AC > FG$

(ii) $CD=1$ unit and $GH=1$ unit

This implies,

\( \mathrm{CD}=\mathrm{GH} \)

(iii) $BC = 1$ unit and $EH = 3$ units

This implies,

$BC < EH$