Question

Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B respectively. Are these lines parallel ?

Answer 1

Hint: We can solve this question by drawing the diagram. First we have to draw the line segment of given length. Then we have to draw the perpendiculars at both the ends. Then we have to check whether the lines are parallel or not by checking the parallel line conditions.

Complete step-by-step solution:
The conditions to check whether the lines are parallel or not.
If the corresponding angles, the angles that are on the same corner at each intersection, are equal, then the lines are parallel.
The second is if the alternate interior angles, the angles that are on opposite sides of the transversal and inside the parallel lines, are equal, then the lines are parallel.
Now to solve our questions we have to follow the following steps.
1.Draw a line segment AB = 4 cm.

2.Taking 4 as centre and radius more than \[\dfrac{1}{2}\] AB draw an arc say it intersects AB at E.

3.Taking E as centre and with the same radius as above draw an arc which intersects the previous arc at F.

4.Again, taking F as centre and with the same radius as above draw an arc which intersects the previous arc at G.

5.Taking G and F are centres, draw arcs which intersect each other at H.

6.Join AH. Thus, AC is perpendicular to AB at A.
 

7. Next we have to draw the perpendicular line at point B say line AD.
8. By following the above process we can draw a perpendicular line at B.

9. Now we can see the angles at both corners A and B are the same i.e.,\[{{90}^{\circ }}\].
10. so we can conclude that both lines Ac and AD are parallel to each other and perpendicular to A and B.

Note: We can draw the perpendicular lines at \[{{90}^{\circ }}\] as AB is a straight line. But for more accuracy we use this arcs method to solve the problem. Be careful while drawing arcs otherwise the whole diagram will change. In this type of problem diagram is most important to solve.