Constructing a parallelogram with one side, one angle and one diagonal — 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 one side, one angle and one diagonal of a parallelogram are given.

Example:

Construct a parallelogram

$JUMP$ with

$JU$

$=$

$8.5$

$cm$ ,

$JM$

$=$

$9$

$cm$ and

$\angle JUM$

$=$

$75^{\circ}$ . Also, find its area.

Construction:

Step 1: Draw a line segment

$JU$

$=$

$8.5$

$cm$ .

Step 2: With

$U$ as centre, mark an angle

$75^{\circ}$ using a protractor and mark it as

$X$ . Join

$QX$ .

Step 3: With

$J$ as centre, draw an arc of radius

$9$

$cm$ intersecting

$QX$ at

$M$ . Join

$JU$ .

Step 4: Measure

$UM$ , and with

$J$ as centre, draw an arc of radius that is equal to the measure of

$UM$ .

Step 5: With

$M$ as centre, draw an arc of radius

$8.5$

$cm$ intersecting the previous arc at

$P$ .

Step 6: Join

$MP$ and

$MJ$ .

Step 7:

$JUMP$ is the required parallelogram. The measure of

$MA$ gives the height of the parallelogram

$JUMP$ .

Area calculation:

Area of the parallelogram

$=$

$base \times height$ square units

$=$

$8.5 \times 5.6$

$=$

$47.60$

$cm^2$

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13. Constructing a parallelogram with one side, one angle and one diagonal

Theory: