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Mathematics

Construct an angle PQR = 60°. Draw a line parallel to PQ at a distance of 3 cm from it and another line parallel to QR at a distance of 3.5 cm from it. Mark the point of intersection of these parallel lines as A.

Quadrilaterals Constructions

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Answer

Steps:

  1. Draw a line segment QR of any suitable length.

  2. With Q as centre, draw an arc of any suitable radius which cuts QR at point I.

  3. With I as centre and the same radius as taken in step 2, draw one more arc which cuts the previous arc.

  4. Join Q with previous intersecting point and produce upto any point P.
    Angle PQR = 60°.

  5. At any point C in line PQ, draw CX perpendicular to PQ.

  6. With C as centre and radius equal to 3 cm, draw an arc which cuts CX at point D.

  7. At point D, draw DE perpendicular to CX.

  8. Produce DE upto any point F.
    EF is the parallel line to PQ.

  9. At any point B in line QR, draw BY perpendicular to QR.

  10. With B as centre and radius equal to 3.5 cm, draw an arc which cuts BY at point G.

  11. At point G, draw GJ perpendicular to BY.

  12. Produce GJ upto any point H.
    HJ is the parallel line to QR.

  13. HJ and EF intersect at point A.

Construct an angle PQR = 60°. Draw a line parallel to PQ at a distance of 3 cm from it and another line parallel to QR at a distance of 3.5 cm from it. Mark the point of intersection of these parallel lines as A. Constructions, Concise Mathematics Solutions ICSE Class 8.

Hence, A is the point of intersection of the parallel lines.

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