Question

Construct the following quadrilateral: Parallelogram $\text{HEAR}$ where$\text{HE = 5 cm}$, $\text{EA = 6 cm}$ and$\angle R=85°$.

Answer 1

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

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

$$\begin{gathered} \text{HE = AR = 5 cm} \\ \text{AE = HR = 6 cm} \end{gathered}$$

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

Step 1: Draw a line segment$\text{HR = 6 cm}$,

Step 2: Draw a ray $\text{RX}$ from point$\text{R}$, making an angle of $85°$ with line segment $\text{HR}$ -

Step 3: Take an arc of radius $\text{5 cm}$ on the compass and cut it from the point$\text{R}$, which intersects ray$\text{RX}$ at $\text{H}$ -

Step 4: Using the arc of radius$\text{5 cm}$. cut an arc from the point$\text{H}$, and then take an arc of radius $\text{6 cm}$ on the compass and cut another arc from a point$\text{A}$ which intersects the previous arc from at point$\text{E}$ -

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