Question

Draw a line segment PQ = 7 cm. Draw lines perpendicular to PQ through A and B (AL and

BM).Are AL and BM parallel?​

Answer 1

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MATHS

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

State Yes or No.

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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.