Choose whether the given statement is true or false.

Draw a line AB of length 8 cm. At each end of this line segment, draw a line perpendicular to AB. Are these two lines parallel?

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True

False

answer is A.

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Detailed Solution

Firstly, Let us draw a line segment AB of length 8 cm

Now take any radius with A as centre and draw an arc such that it intersects the line AB at points C and D.
After that by taking C and D as centres and radius greater than AC, draw two arcs which intersects each other at G.
Now, join the line AG and extend it in both the directions to I and J.
Do the same steps by taking B as center and we get a line KL perpendicular to AB.
Here we can see that IJ and KL are the lines perpendicular at A and B, respectively.
From the below figure we can observe that, ∠IAB=

90^{0}

and ∠ABK =

90^{0}

So, ∠IAB = ∠ABK
We know that, when the two lines are intersected by a third line, then the two alternate interior angles are equal.
Since, ∠IAB = ∠ABK
Hence, IJ and KL are parallel.
So, option (1) is correct for this question.
Hence, the given statement is true.