Draw a line segment 6.4 cmlong and draw its perpendicular bisector. Measure the length of each part.

Draw a line segment 6.4 cmlong and draw its perpendicular bisector. Me

1.	Draw a line segment 6.4 cmlong and draw its perpendicular bisector. Measure the length of each part.
Answer» Solution :STEPS OF CONSTRUCTION (i) Draw a ling segment `AB=6.4` cm. (ii) With `A` as centre and a radius equal to more than half of `AB`, draw two arcs, one above `AB` and the other below `AB.` (iii) With `B` as centre and the same radius, draw two arcs, cutting the previously drawn arcs at points `C` and `D` respectively. (iv) Join `CD` is the required perpendicular bisector of AB at the point O. On measuring, we find that `OA=3.2` cm and `OB=3.2` cm Also, `angleAOC=angle BOC=90^(@)` JUSTIFICATION : Join AC, AD, BC and BD. In `Delta CAD` and `Delta CBD`, we have `AC=BC` (arcs of equal RADII) `AD=BD` (arcs of equal radii) `CD=CD` (common) `:. Delta CAD cong Delta CBD` (SSS-criteria) `:. angle ACO = angle BCO` (c.p.c.t.). Now, in `Delta AOC` and `Delta BOC`, we have `AC=BC` (arcs of equal radii) `angleACO=angle BCO` (PROVED above) `CO=CO` (common) `:. Delta AOC cong Delta BOC` (SAS-criteria). Hence, `AO=BO` and `angleAOC=angleBOC`. But, `angleAOC+angleBOC=180^(@)` (LINEAR pair axiom) `:. angle AOC=angle BOC=90^(@)`. Hence, COD is the perpendicular disector of `angleAOB`.