Question

Construct the following quadrilateral: Parallelogram $\text{MORE}$ where $\text{OR = 6 cm}$, $\text{ER = 4.5 cm}$ and $\text{EO = 7.5 cm}$.

Answer 1

Constructing the quadrilateral $\text{MORE}$:

Let's draw a rough sketch of a parallelogram $\text{MORE}$, to get an idea about the parallelogram -

By the properties of the parallelogram, we know that opposite sides are equal, therefore

$$\begin{gathered} \text{ER = MO = 4.5 cm} \\ \text{ME = OR = 6 cm} \\ \text{EO = 7.5 cm} \end{gathered}$$

Let's construct the parallelogram $\text{MORE}$ using the information given in the question -

Step 1: Draw a line segment $\text{ER = 4.5 cm}$

Step 2: Take an arc of radius $\text{6 cm}$ on the compass & cut an arc from point $\text{R}$, then change the radius to $\text{7.5 cm}$ and cut another arc from point $\text{E}$ which intersect the previous arc at point$O$ and then join $\text{EO , RO}$.

Step 3: Take an arc of radius $\text{6 cm}$ on the compass & cut an arc from point $\text{E}$, then change the radius to $\text{4.5 cm}$ and cut another arc from point $\text{O}$ which intersect the previous arc at point $\text{M}$.

Step 4: Join $\text{OM , ME}$ to get the required quadrilateral -

Hence, $\text{MORE}$ is the required parallelogram.