Selina solutions for Concise Mathematics Class 8 ICSE chapter 18 - Constructions [Latest edition]

Given below are the angles x and y.

Without measuring these angles, construct :

(i)

(ii)

(iii)

Given below are the angles x, y, and z.

Without measuring these angles construct :

(i) (ii) (iii)

Draw a line segment BC = 4 cm. Construct angle ABC = 60°.

Construct angle ABC = 45° in which BC = 5 cm and AB = 4.6 cm.

Construct angle ABC = 90°. Draw BP, the bisector of angle ABC. State, the measure of angle PBC.

Draw angle ABC of any suitable measure.

(i) Draw BP, the bisector of angle ABC.
(ii) Draw BR, the bisector of angle PBC and draw BQ, the bisector of angle ABP.
(iii) Are the angles ABQ, QBP, PBR and RBC equal?
(iv) Are the angles ABR and QBC equal?

Draw a line segment AB of length 5.3 cm. Using two different methods bisect AB.

Draw a line segment PQ = 4.8 cm. Construct the perpendicular bisector of PQ.

In each of the following, draw perpendicular through point P to the line segment AB :

(i)

(ii)

(iii)

Draw a line segment AB = 5.5 cm. Mark a point P, such that PA = 6 cm and PB = 4.8 cm. From point P, draw a perpendicular to AB.

Draw a line segment AB = 6.2 cm. Mark a point P in AB such that BP = 4 cm. Through point P draw perpendicular to AB.

Draw a line AB = 6 cm. Mark a point P anywhere outside the line AB. Through point P, construct a line parallel to AB.

Draw a line MN = 5.8 cm. Locate a point A which is 4.5 cm from M and 5 cm from N. Through A draw a line parallel to line MN.

Draw a straight line AB = 6.5 cm. Draw another line which is parallel to AB at a distance of 2.8 cm from it.

Construct an angle PQR = 80°. Draw a line parallel to PQ at a distance of 3 cm from it and another line parallel to QR at a distance of 3.5 cm from it. Mark the point of intersection of these parallel lines as A.

Draw an angle ABC = 60°. Draw the bisector of it. Also, draw a line parallel to BC a distance of 2.5 cm from it.
Let this parallel line meet AB at point P and angle bisector at point Q. Measure the length of BP and PQ. Is BP = PQ?

Construct an angle ABC = 90°. Locate a point P which is 2.5 cm from AB and 3.2 cm from BC.

Construct a quadrilateral ABCD; if:

AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and angle ABC = 75°.

Construct a quadrilateral ABCD; if:

AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and ∠BCD = 60°.

Construct a quadrilateral ABCD; if:

AB = 8 cm, BC = 5.4 cm, AD = 6 cm, ∠A = 60° and ∠B = 75°.

Construct a quadrilateral ABCD; if:

AB = 5 cm, BC = 6.5 cm, CD =4.8 cm, ∠B = 75° and ∠C = 120°.

Construct a quadrilateral ABCD; if:

AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

Construct a quadrilateral ABCD; if:

AB = AD = 5cm, BD = 7 cm and BC = DC = 5.5 cm

Construct a parallelogram ABCD, if :

AB = 3.6 cm, BC = 4.5 cm and ∠ABC = 120°.

Construct a parallelogram ABCD, if :

BC = 4.5 cm, CD = 5.2 cm and ∠ADC = 75°.

Construct a parallelogram ABCD, if :

AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.

Construct a parallelogram ABCD, if :

AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.

Construct a parallelogram ABCD, if :

diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75°.

Construct a parallelogram ABCD, if :

lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is 45°.

Construct a parallelogram ABCD, if :

lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between them is 60°.

Construct a rectangle ABCD; if :

AB = 4.5 cm and BC = 5.5 cm.

Construct a rectangle ABCD; if :

BC = 6.1 cm and CD = 6.8 cm.

Construct a rectangle ABCD; if :

AB = 5.0 cm and diagonal AC = 6.7 cm.

Construct a rectangle ABCD; if :

AD = 4.8 cm and diagonal AC = 6.4 cm.

Construct a rectangle ABCD; if :

each diagonal is 6 cm and the angle between them is 45°.

Construct a rectangle ABCD; if :

each diagonal is 5.5 cm and the angle between them is 60°.

Construct a rhombus ABCD, if ;

AB = 4 cm and ∠B = 120°.

Construct a rhombus ABCD, if ;

BC = 4.7 cm and ∠B = 75°.

Construct a rhombus ABCD, if ;

CD = 5 cm and diagonal BD = 8.5 cm.

Construct a rhombus ABCD, if ;

BC = 4.8cm, and diagonal AC = 7cm.

Construct a rhombus ABCD, if ;

diagonal AC = 6 cm and diagonal BD = 5.8 cm.

Construct a rhombus ABCD, if ;

diagonal AC = 4.9 cm and diagonal BD = 6 cm.

Construct a rhombus ABCD, if ;

diagonal AC = 6.6 cm and diagonal BD = 5.3 cm.

Construct a square, if :

it's one side is 3.8 cm.

Construct a square, if :

its each side is 4.3 cm.

Construct a square, if :

one diagonal is 6.2 cm.

Construct a square, if :

each diagonal is 5.7 cm.

Construct a quadrilateral ABCD in which ; ∠A = 120°, ∠B = 60°, AB = 4 cm, BC = 4.5 cm and CD = 5 cm.

Construct a quadrilateral ABCD, such that AB = BC = CD = 4.4 cm, ∠B = 90° and ∠C = 120°.

Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and ∠DAB = 60°. In the same figure draw the bisector of angle DAB and let it meet DC at point P. Measure angle APB.

Draw a parallelogram ABCD, with AB = 6 cm, AD = 4.8 cm and ∠DAB = 45°. Draw the perpendicular bisector of side AD and let it meet AD at point P. Also, draw the diagonals AC and BD; and let them intersect at point O. Join O and P. Measure OP.

Using a ruler and compasses only, construct a rhombus whose diagonals are 8 cm and 6 cm. Measure the length of its one side.