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Question

Construct the following quadrilateral: Parallelogram HEAR whereHE=5cm, EA=6cm andR=85°.


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Solution

Let's draw a rough sketch of a parallelogramHEAR, to get an idea about the parallelogram -

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

HE=AR=5cmAE=HR=6cm

Let's construct the parallelogramHEAR using the information given in the question -

Step 1: Draw a line segmentHR=6cm,

Step 2: Draw a ray RX from pointR, making an angle of 85° with line segment HR -

Step 3: Take an arc of radius 5cm on the compass and cut it from the pointR, which intersects rayRX at H -

Step 4: Using the arc of radius5cm. cut an arc from the pointH, and then take an arc of radius 6cm on the compass and cut another arc from a pointA which intersects the previous arc from at pointE -

Hence, HEAR is the required parallelogram.


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