Q1. Construct the following quadrilaterals:.
(iii) Parallelogram HEAR
HE = 5 cm
EA = 6 cm
∠R = 85°
Given that HEAR is a parallelogram,.
HE = 5 cm
EA = 6 cm
∠R = 85°
We know that the diagonally opposite angles of a parallelogram are equal.
Therefore, ∠E = ∠R = 85°
The 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 the centre and radius of 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 85° at E. As EA = 6 cm, draw an arc with O as the centre and radius = 6 cm. We get to point A.
Step 2. Construct an angle of (180°-85° = 95°) at A. (Adjacent angles in a parallelogram are supplementary.)
Step 3. Construct an angle of (180°-85° = 95°) at H. This ray intersects the previous one at R.
HEAR is the required parallelogram.