Practical Geometry - Exercise 4.3 - NCERT Solutions

Chapter 4: PRACTICAL GEOMETRY

Exercise 4.3

Q.1 Construct the following quadrilaterals.

(i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

Sol. Step 1: Draw a line segment MO of length 6 cm and an angle 105° at point O. Now, keep O as centre and cut an arc OR of 4.5 cm from this ray.

Step 2: Draw an angle of 105° at point R.

Step 3: Now, draw an angle of 60° at point M such that it intersects the ray drawn in previous step at point E. Complete the quadrilateral MORE.

(ii) Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

Sol. We know that sum of angles of a quadrilateral is 360áµ’.

So, ∠P + ∠L + ∠A + ∠N = 360ᵒ.

90ᵒ + ∠L + 110ᵒ + 85ᵒ = 360ᵒ

Thus, ∠L = 75ᵒ

Step 1: Draw line segment PL of length 4 cm. Now, draw an angle of 75áµ’ at point L; cut a line segment LA of 6.5 cm from point L.

Step 2: Draw an angle of 110áµ’ at point A.

Step 3: From point P, draw an angle of 90áµ’. This ray will meet the ray from point A intersecting at point N.

(iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

Sol. Step 1: Draw a line segment HE of length 5 cm and an angle of 85° at point E. Now, keep E as centre and cut an arc EA of 6 cm from this ray.

Step 2: Keep H as centre and draw an arc of radius 6 cm on the opposite side of point E. Draw another arc keeping A as centre of radius 5 cm, such that it intersects the previous drawn arc. Let the point of intersection be R.

Step 3: To complete the quadrilateral HEAR, join H and A to R.

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

Sol. Step 1: Draw a line segment OK of length 7 cm and an angle of 90° at point K. Now, keep K as centre and cut an arc KA of 5 cm from this ray.

Step 2: Keep O as centre and draw an arc of radius 5 cm on the opposite side of point K. Draw another arc keeping centre as A of radius 7 cm, such that it intersects the previously drawn arc. Let the point of intersection be Y.

Step 3: To complete the rectangle OKAY, join A and O to Y.