Constructing a parallelogram with two diagonals and one included angle — lesson. Mathematics State Board, Class 8.

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Working rule to construct a parallelogram:

Let us discuss the working rule to construct a parallelogram when the measure of two diagonals and one included angle of a parallelogram are given.

Example:

Construct a parallelogram

$PQRS$ with

$PR$

$=$

$10$

$cm$ ,

$QS$

$=$

$8$

$cm$ and

$\angle POQ$

$=$

$120^{\circ}$ . Also, find its area.

Construction:

Step 1: Draw a line segment

$PR$

$=$

$10$

$cm$ .

Step 2: Mark the midpoint of the line segment

$PR$ as

$O$ .

Step 3: Draw a line

$XY$ through

$O$ such that

$\angle POQ$

$=$

$120^{\circ}$ .

Step 4: With

$O$ as centre, draw two arcs each of radii

$4$

$cm$ on either side of

$PR$ intersecting

$XY$ at

$Q$ and

$S$ .

Step 5: Join

$PQ$ ,

$QR$ ,

$RS$ and

$SP$ .

Step 6:

$PQRS$ is the required parallelogram. The measure of

$SA$ gives the height of the parallelogram

$PQRS$ .

Area calculation:

Area of the parallelogram

$=$

$base \times height$ square units.

$=$

$8 \times 4.3$

$=$

$34.40$

$cm^2$

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12. Constructing a parallelogram with two diagonals and one included angle

Theory: