Question

Draw a parallelogram \[ABCD\] in which \[AB=6.5cm\], \[AD=4.8cm\] and \[\angle BAD={{70}^{\circ }}\]. Also, measure its diagonals.

Answer 1

Hint: We are given with the measure of two sides. In a parallelogram, opposite sides are equal. So it means that we are given with all the four sides of the parallelogram. In order to draw the parallelogram, draw the base with measurement and then construct the angle upon it then measure it according to the measure of the other side.

Complete step-by-step solution:
Let us learn about the properties of the parallelogram. There are seven basic properties:
 Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
If one of the angles is a right angle, then all of the angles are right angles.
The diagonals of a parallelogram bisect each other.
Each diagonal separates the parallelogram into two congruent triangles.
Now let us start constructing our parallelogram.
Since it is a parallelogram,
\[\begin{align}
  & AB=CD=6.5cm \\
 & AD=BC=4.8cm \\
\end{align}\]
Given, \[\angle BAD={{70}^{\circ }}\]

Steps of construction:
Draw \[AD\] such that \[AD=4.8cm\].

Make an angle measuring \[{{70}^{\circ }}\] at \[A\] and cut an arc of \[6.5cm\] and name it as \[B\]

From \[B\] cut an arc of \[4.8cm\] and \[6.5cm\] from \[D\] and name it as \[C\].

Join\[AB,BC,CD\].

Measure the diagonals with the ruler.

So, we get the approx diagonal lengths as AC = 7.87 and BD = 5.51.

Note: There are two types of parallelograms, if all of the sides are equal in a parallelogram, then it is called a rhombus. There are two other special types of parallelograms. They are square and rectangle. They are considered as parallelograms because they satisfy the conditions for a polygon to be a parallelogram.