Question

Draw a line segment XY of length 8 cm. At X and Y, draw perpendiculars to XY using
compasses and ruler. Are the lines parallel to each other?
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

ANSWER

Step I: Take a convenient radius with A as centre and draw an arc intersecting the line at points W and X.

Step II: With W and X as centres and radius greater than AW, construct two arcs intersecting each other at M.

Step III: Join AM and extend it in both directions to P and Q.

Step IV: Take a convenient radius with B as centre and draw an arc intersecting the line at points Y and Z.

Step V: With Y and Z as centres and a radius greater than YB, construct two arcs intersecting each other at N.

Step VI: Join BN and extend it in both directions to S and R.

Let the lines perpendicular at A and B be PQ and RS, respectively.

Since, ∠QAB=90

°

and ∠ABR=90

°

Therefore, ∠QAB=∠ABR

When two parallel lines are intersected by a third line, the two alternate interior angles are equal.

Since, ∠QAB=∠ABR

Therefore, PQ and RS are parallel.