## Chapter 8 Quadrilateral: Constructions and Types Set 8.1

Construct the following quadrilaterals of given measures.

Question 1.

In âˆ†MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, mâˆ M = 58Â°, mâˆ O = 105Â°, mâˆ R = 90Â°.

Solution:

Question 2.

Construct âˆ†DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.

Solution:

Question 3.

In âˆ†ABCD, l(AB) = 6.4 cm, l(BC) = 4.8 cm, mâˆ A = 70Â°, mâˆ B = 50Â°, mâˆ C = 140Â°.

Solution:

Question 4.

Construct â‚¹LMNO such that

l(LM) = l(LO) = 6 cm,

l(ON) = l(NM) = 4.5 cm, l(OM) = 7.5 cm.

Solution:

**Intext Questions and Activities**

Question 1.

Construction of a triangle:

Construct the triangles with given measures. (Textbook pg. no. 41)

i. âˆ†ABC: l(AB) = 5 cm, l(BC) = 5.5, l(AC) = 6 cm.

Solution:

Steps of construction:

Step 1 : As shown in the rough figure, draw seg BC of length 5.5 cm as the base.

Step 2 : By taking a distance of 5 cm on the compass and placing the metal tip of the compass on point B, draw an arc on one side of BC.

Step 3 : By taking a distance 6 cm on the compass and placing the metal tip of the t compass on point C and draw an arc â€™ such that it intersects the previous arc. Name the point as A.

Step 4 : Draw segments AB and AC to get the triangle. âˆ†ABC is the required triangle.

ii. âˆ†DEF: mâˆ D = 35Â°, mâˆ F = 100Â°, l(DF) = 4.8 cm.

Solution:

Steps of construction:

Step 1 : As shown in the rough figure, draw seg DF of length 4.8 cm as the base.

Step 2 : Placing the centre of the protractor at point D, mark point P such that mâˆ PDF = 35Â°.

Step 3 : Placing the centre of the protractor at point F, mark point Q such that mâˆ QFD = 100Â°.

Step 4 : Draw ray DP and ray FQ. Name their point of intersection as E.

âˆ†DEF is required triangle.

iii. âˆ†MNP: l(MP) = 6.2 cm, l(NP) = 4.5 cm, mâˆ P = 75Â°.

Solution:

Steps of construction:

Step 1 : As shown in the rough figure, draw seg PN of length 4.5 cm as the base.

Step 2 : Placing the centre of the protractor at point P, mark point Q such that mâˆ QPN = 75Â°.

Step 3 : By taking a distance of 6.2 cm on the compass and placing the metal tip at point P, draw an arc on ray PQ. Name the point as M.

Step 4 : Draw seg MN to get the triangle. âˆ†MNP is the required triangle.

iv. âˆ†XYZ: mâˆ Y = 90Â°, l(XY) = 4.2 cm, l(XZ) = 7 cm.

Solution:

Steps of construction:

Step 1 : As shown in the rough figure, draw seg XY of 4.2 cm as the base.

Step 2 : Placing the centre of the protractor at point Y, mark point Q such that mâˆ QYX = 90Â°.

Step 3 : By taking a distance of 7 cm on the compass and placing the metal tip on point X, draw an arc on ray YQ. Name the point as Z.

Step 4 : Draw seg XZ to get the triangle. âˆ†XYZ is the required triangle.