(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) $\mathrm{BC}" "> # Study the diagram. The line$ 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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Updated on: 10-Oct-2022

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