onstruct a parallelogram HEAR, where HE= 5cm,

EA= 6 cm and <R= 75°.​

1 thought on “onstruct a parallelogram HEAR, where HE= 5cm,<br /><br />EA= 6 cm and <R= 75°.​”

1. Answer:

   Step-by-step explanation:

   Given, HEAR is a parallelogram.

   HE = 5 cm

   EA = 6 cm

   ∠R = 75°

   We know, Diagonally opposite angles of a parallelogram are equal.

   Therefore, ∠E = ∠R = 75°

   And, Opposite sides of a parallelogram are equal and parallel to each other.

   Therefore, AR = HE = 5 cm

   RH = EA = 6 cm

   Steps of construction:

   Step 1. Draw a line segment HE = 5 cm. Construct an angle of 85° at E. As EA = 6 cm, draw an arc with O as center and radius = 6 cm. We get to point A.

   Step 2. With A as centre, draw an arc of radius = AR = HE = 5 cm.

   Step 3. With H as centre , draw an arc of radius = HR = EA = 6 cm. The intersection of this arc with the previous arc is R.

   Step 4. Join R to H and R to A.

   HEAR is the required parallelogram.

   Alternatively,

   Steps of construction

   Step 1. Draw a line segment HE = 5 cm. Construct an angle of 75° at E. As EA = 6 cm, draw an arc with O as center and radius = 6 cm. We get to point A.

   Step 2. Construct an angle of (180°-75° = 105°) at A. (Adjacent angles in a parallelogram are supplementary)

   Step 3. Construct an angle of (180°-75° = 105°) at H. This ray intersects the previous one at R.

   HEAR is the required parallelogram.

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