Question

14

The perpendicular distances between the pairs of opposite sides of a parallelogram
ABCD are 3 cm and 4 cm and one of its angles measures 60°. Using ruler and compasses
only, construct ABCD.
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Answer 1

Answer:

ABCD is the required parallelogram.

Step-by-step explanation:

1. Draw a base line AP.

2. From A take some random distance in compass and draw arc on both sides of the . Now without changing the distance in compass draw arcs from point P so that it intersects earlier arcs.

.Draw the line passing through these intersecting points, to get a perpendicular to the line AP.

3 Take distance of 4 cm in compass and mark an arc on the perpendicular above the line. Draw a line parallel to line AQ passing through through this point.

4. From point A measure an angle of 60 degree and draw the line which intersect above drawn line at some point label it as D.

5. Using the procedure given in step 2 again draw a perpendicular to line AD.

6. Take distance of 3 cm in compass and mark an arc on the perpendicular above the line. Draw a line parallel to line AD passing through through this arc which intersect the line AP at some point label it as B and to other line at point C.

ABCD is the required parallelogram.

Answer 2

Steps of construction:

(i) Draw AC = 6cm

(ii) Find the mid-point O of AC. [Since, diagonals of || gm bisect each other]

(iii) Draw line POQ such that POC = 60o and OB = OD = ½ BD = ½ x 8cm = 4cm

So, from OP cut OD = 4cm and from OQ cut OB = 4cm

(iv) Join AB, BC, CD and DA.

Thus, ABCD is the required parallelogram.

(v) Measure the length of side AD = 6.1cm