Question

draw a line segment a b of length 5 cm and at A and B construct line perpendicular to a b also draw the perpendicular bisector of a b are these 3 lines parallel to each other justify your answer

Answer 1

The solution is attached as a word file.

aed35e7bb2022e8445c0e1c2f064408c.doc

Answer 2

IMAGE

Here the length of AB = 5cm  

DA is perpendicular to AB.  

EB is perpendicular to AB.  

Two lines perpendicular to same line are parallel to each other.  

Also $\angle1 =\angle 3 = 90^{o}$

So $\angle1 + \angle3 = 180^{o}$

If the sum of co interior angles = 180°, the lines are parallel.  

Hence AD || BE  

Now we construct the perpendicular bisector of AB which intersects AB at C  

Again  

$\angle1= \angle2 = 90^{o}$

So  

$\angle1 + \angle2 = 180^{o}$

We know If the sum of co interior angles = 180°, the lines are parallel.  

Hence AD || CF  

Now BE ||AD || CF  

Hence all the three lines are parallel to each other.