Construct Parallelogram HEAR where HE = 5 cm, EA = 6 cm, $∠ R = 85^{\circ}$ .

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Solution

Concept :
HEAR is a parallelogram
$\Rightarrow H E = R A = 5 c m$ and $E A = H R = 6 c m$ [Since opposite sides of a parallelogram are equal]
Also, $∠ R = ∠ E = 85^{\circ}$ [Since opposite angles of a parallelogram are equal]
$∠ H = (180 - 85)^{\circ} = 95^{\circ}$ [Adjacent angles of a parallelogram are supplementry]

Steps of Construction:

1. Draw line segment HE= 5cm.
2. At E construct an angle of $85^{\circ}$ . Draw an arc of length 6 cm intersecting the ray from E at A.
3. At A construct an angle of $95^{\circ}$ . Draw an arc of length 5 cm intersecting the ray from A.
4. With H as centre draw an arc of length 6 cm which intersects the earlier arc. Let it be R
5. Join HR and AR to complete quadrilateral HEAR.

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Construct Parallelogram HEAR where HE = 5 cm, EA = 6 cm, $∠ R = 85^{\circ}$ . [4 MARKS]

∠ R = 85^{\circ}

Question 3
Construct the Parallelogram HEAR where
HE=5cm, EA=6cm, $∠ R = 85^{\circ}$

H E A R

H E = 5 c m

E A = 6 c m

∠ R = 85^{o}

Construct the following quadrilaterals.

(i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

(ii) Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

(iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

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