Question

Try to draw quadrilateral ABCD of these specifications:

(i) AB = 7 cm, BC =5 cm, CD = 4 cm, ∠B = 60°, ∠C = 140°.

(ii) AB = 8 cm, BC = 6 cm, CD = 5.5 cm, DA = 3 cm, ∠B = 50°.

(iii) AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm.

Answer 1

(i) Here is the rough sketch of the required quadrilateral.

The steps of construction are as follows:

(1) Draw a line segment BC of length 5 cm.

(2) At point B, draw ∠PBC of measure 60°.

(3) At point C, draw ∠QCB of measure 140°.

(4) Taking B as the centre and 7 cm as the radius, draw an arc which intersects ray BP at point A.

(5) Taking C as the centre and 4 cm as the radius, draw an arc which intersects ray CQ at point D.

(6) Join AD.

ABCD is the required quadrilateral.

(ii) Here is the rough sketch of the required quadrilateral.

The steps of construction are as follows:

(1) Draw a line segment AB of length 8 cm.

(2) At point B, draw ∠PBA of measure 50°.

(3) Taking B as the centre and 6 cm as the radius, draw an arc which intersects BP at point C.

(4) Taking C as the centre and 5.5 cm as the radius, draw an arc on the left side of ray BP.

(5) Taking A as the centre and 3 cm as the radius, draw an arc which intersects the previously drawn arc at point D.

(6) Join AD and CD.

ABCD is the required quadrilateral.

(iii) Here is the rough sketch of the required quadrilateral.

The steps of construction are as follows:

(1) Draw a line segment DC of length 5 cm.

(2) Taking D as the centre and 7.5 cm as the radius, draw an arc on the upper side of line segment CD.

(3) Taking C as the centre and 4.5 cm as the radius, draw an arc which intersects the previously drawn arc at point B.

(4) Join BD and BC.

(5) Taking B as the centre and 8.5 cm as the radius, draw an arc on the left side of point B.

(6) Taking D as the centre and 6 cm as the radius, draw an arc which intersects the previously drawn arc at point A.

(7) Join AD and AB.

ABCD is the required quadrilateral.