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**Chapter 4: PRACTICAL GEOMETRY**

**Exercise 4.3**

**Q.1 Construct the following quadrilaterals.**

**(i) Quadrilateral MORE**

**MO = 6 cm**

**OR = 4.5 cm**

**âˆ M = 60Â°**

**âˆ O = 105Â°**

**âˆ R = 105Â°**

** Sol.** Step 1: Draw a line segment MO of length 6 cm and an angle 105Â° 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 105Â° at point R.

Step 3: Now, draw an angle of 60Â° 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**

**âˆ P = 90Â°**

**âˆ A = 110Â°**

**âˆ N = 85Â°**

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

So, âˆ P + âˆ L + âˆ A + âˆ N = 360áµ’.

90áµ’ + âˆ L + 110áµ’ + 85áµ’ = 360áµ’

Thus, âˆ L = 75áµ’

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**

**âˆ R = 85Â°**

** Sol.** Step 1: Draw a line segment HE of length 5 cm and an angle of 85Â° 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 90Â° 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.

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