Mathematics
The perpendicular distances between the pair of opposite sides of a parallelogram, are 3 cm and 4 cm, and one of its angles measures 60°. Using ruler and compasses only, construct the parallelogram.
Rectilinear Figures
1 Like
Answer
Steps of construction :
Draw a straight line PQ, take a point A on it.
At A, construct ∠QAF = 60°.
At A, draw AE ⊥ PQ, from AE cut off AN = 3 cm.
Through N draw a straight line parallel to PQ to meet AF at D.
At A, draw AG ⊥ AD, from AG cut off AM = 4 cm.
Through M, draw a straight line parallel to AD to meet AQ at B and ND at C.
Join AB, BC, CD and DA.
Hence, ABCD is the required parallelogram.
Answered By
1 Like
Related Questions
Using ruler and compasses only, construct the quadrilateral ABCD, having given AB = 5 cm, BC = 2.5 cm, CD = 6 cm, ∠BAD = 90° and diagonal BD = 5.5 cm.
Using ruler and compasses only, construct a parallelogram ABCD using the following data :
AB = 6 cm, AD = 3 cm and ∠DAB = 45°. If the bisector of ∠DAB meets DC at P, prove that ∠APB is a right angle.
Draw parallelogram ABCD with the following data :
AB = 6 cm, AD = 5 cm and ∠DAB = 45°.
Let AC and DB meet in O and let E be the mid-point of BC. Join OE. Prove that :
(i) OE // AB
(ii) OE = AB
Using ruler and compasses only, construct a rectangle each of whose diagonals measure 6 cm and the diagonals intersect at an angle of 45°.