Question

# Count the number of line segments drawn in each of the following figures and name them. (i) Figure (ii) Figure (iii) Figure (iv) Figure

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Solution

## (i) There are 6 line segments. These are: $\overline{AB}\left(withendpointsAandB\right)\phantom{\rule{0ex}{0ex}}\overline{AC}\left(withendpointsAandC\right)\phantom{\rule{0ex}{0ex}}\overline{AD}\left(withendpointsAandD\right)\phantom{\rule{0ex}{0ex}}\overline{BC}\left(withendpointsBandC\right)\phantom{\rule{0ex}{0ex}}\overline{BD}\left(withendpointsBandD\right)\phantom{\rule{0ex}{0ex}}\overline{CD}\left(withendpointsCandD\right)\phantom{\rule{0ex}{0ex}}$ (ii) There are 10 line segments. These are: $\overline{AB}\left(withendpointsAandB\right)\phantom{\rule{0ex}{0ex}}\overline{BC}\left(withendpointsBandC\right)\phantom{\rule{0ex}{0ex}}\overline{CD}\left(withendpointsCandD\right)\phantom{\rule{0ex}{0ex}}\overline{AD}\left(withendpointsAandD\right)\phantom{\rule{0ex}{0ex}}\overline{AC}\left(withendpointsAancC\right)\phantom{\rule{0ex}{0ex}}\overline{BD}\left(withendpointsBandD\right)\phantom{\rule{0ex}{0ex}}\overline{AO}\left(withendpointsAandO\right)\phantom{\rule{0ex}{0ex}}\overline{CO}\left(withendpointsCandO\right)\phantom{\rule{0ex}{0ex}}\overline{BO}\left(withendpointsBandO\right)\phantom{\rule{0ex}{0ex}}\overline{DO}\left(withendpointsDandO\right)\phantom{\rule{0ex}{0ex}}$ (iii) There are 6 line segments. They are: $\overline{AB},\overline{AF},\overline{FB},\phantom{\rule{0ex}{0ex}}\overline{EC},\overline{ED},\overline{DC}\phantom{\rule{0ex}{0ex}}$ (iv) There are 12 line segments. They are: $\overline{AB},\overline{AD},\overline{AE}\phantom{\rule{0ex}{0ex}}\overline{BC},\overline{BF}\phantom{\rule{0ex}{0ex}}\overline{CG},\overline{CD}\phantom{\rule{0ex}{0ex}}\overline{HG},\overline{HE},\overline{DH}\phantom{\rule{0ex}{0ex}}\overline{EF},\overline{GF}\phantom{\rule{0ex}{0ex}}$

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