Question

Construct a parallelogram ABCD such that $AC=6cm,BD=4.6cm$ and angle between them $45{}^{\circ }$ .

Answer 1

Hint: For construction of a parallelogram we need a protractor, rules, pencil compass. Given lines are diagonals, we need to observe that end points of these lines are the opposite vertices of a parallelogram. By basic knowledge of geometry, we can say that diagonals of parallelograms always bisect each other. So, find the mis-point and draw another line segment passing through the midpoint of the first line segment. By joining the ends of these both line segments we get our required parallelogram ABCD.

Complete step-by-step answer:
Aim: To draw a parallelogram ABCD with lengths of line segments AC, BD as 6 cm, 4.6 cm respectively and angle between them as 45 degrees.
Given $AC=6cm,BD=4.6cm$
First take a ruler and draw a line segment of length 6 cm. Now, mark the end points of this line segment as A, C.
Now, mark a point O at a distance of 3 cm from A to line.
Now, the figure should like as shown below:
 

Now, take a protractor and mark the direction of . Take a compass and draw an arc from O with radius 2.3 cm.
As we know O is mid-point of AC we took AO as 3 cm.
As we also know O is taken midpoint of BD taken, we draw a line of 2.3 cm with ${45}^{\circ }$ with AC.
Now mark the intersection of line and arc as B.

Do the similar way opposite side to get D.
Now repeat the same on the other side of AC and find a point at 2.3 cm with ${45}^{\circ }$ .
Then join the both points B, D and mark the line as BD.
Now the figure will look as follows: -

Now by joining the point AB, BC, CD, DA we get our required parallelogram.

Hence, we constructed our required parallelogram.
Note: The compass may give error of nearly 0.1 cm due to sight error near the ruler whose precision is 0.1 cm. Kindly ignoring that we surely get out required parallelogram ABCD.