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=90

o

So \angle1 + \angle3 = 180^{o}∠1+∠3=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}∠1=∠2=90

o

So

\angle1 + \angle2 = 180^{o}∠1+∠2=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.

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Answer 2

Step-by-step explanation:

1. Draw a line segment AB = 5 cm.

2. With any radius greater than 2.5 cm, and compass fixed at A, draw 2 arcs, one above and one below AB.

3. With the same radius, compass at B, cut the 2 arcs drawn in step 2.

4. The line joining these two arcs is the perpendicular bisector of AB.

i.e. CD is the perpendicular bisector of AB.

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