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,
$BC < EH$
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