Question

Draw a line segment AB of length 5 cm. At A
and B, construct lines perpendicular to AB.
Also, draw the perpendicular bisector of AB.
Are these three lines parallel to each other?
Justify your answer.
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Answer 1

Answer:

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}∠1=∠3=90o

So \angle1 + \angle3 = 180^{o}∠1+∠3=180o

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}∠1=∠2=90o

So  

\angle1 + \angle2 = 180^{o}∠1+∠2=180o

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.  

Step-by-step explanation:

Image given above through picture.

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