Chapter 57, Problem 1A

Trace this line segment two times. On one copy construct a perpendicular bisector of the segment. On the other copy divide the segment into three equal segments.

To determine

To construct:

A perpendicular bisector of the line segment.

To divide: The line segment into three equal parts.

Answer to Problem 1A

Area $\text{A=}\text{1}\text{.72}{\text{in}}^{\text{2}}\text{.}$

Explanation of Solution

Steps of construction:

1. Taking A as a centre and radius more than half of AB, draw arcs on both the above and below the line segment AB as shown in figure (a).
2. Similarly, taking B as a centre and radius same as above draw another arc on both the sides of the line segment that intersects the first pair of arcs as shown in the diagram (b).
3. Join both the arcs by drawing a straight line. Line CD as shown in figure (c), is the perpendicular bisector of line segment AB with O as a centre.

  

Divide the line segment into three equal parts:

Steps of construction:

1. From point A, draw a line segment AC forming an angle with AB as shown in fig(a).
2. On line segment AC with the help of a compass mark three equal arcs D, E and F of any length (b).
3. Connect point F with point B.
4. Now taking F as a centre, draw arcs which intersect the line segment AC at G and BF at H.
5. Repeat the procedure by taking D and E as centre and mark an arc of same radii as shown in figure.
6. With the help of a compass measure the distance GH and mark the same distance from other two arcs as well which intersects the arcs at point K and M respectively.
7. Join E with K and D with M and extending the lines past AB. Thus, line segment AB is divided into three equal parts.