Using ruler and compasses only, construct
a rectangle each of whose diagonals measure
6 cm and the diagonals intersect at an angle
of 45°.
Answers
Step-by-step explanation:
Solutions :- points to be remember. diagonals of rectangle are equal in length. diagnols of rectangle bisect each other. Now explain for construction:- draw a line AB of 6cm. Now make perpendicular bisector of line AB which is at point O. Then from O draw an angle of 45 degree. Produce the angle of 45 degree back also. Now cut the line of length 3cm on both side of 45 degree angle and marked as point C & D. Finally join the line AC, CB, BD & AD. Therefore the figure so obtained ACBD is rectangle. I hope this is helpful for you.
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