## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Objective Type Questions

**Higher Order Thinking Skills (Hots)**

Question 1.

Construct a trapezium ABCD in which AB = 7 cm, BC = 4 cm, CD = 3 cm, ∠B = 60° and AB || DC.

Solution:

Steps of construction :

(i) Draw a line segment AB = 7 cm.

(ii) At B, draw a ray BX making an angle of 60°

and cut off BC = 4 cm.

(iii) At C draw a line CY parallel to AB

making an angle of 120° and cut off CD = 3 cm.

(iv) Join AD.

ABCD is the required trapezium.

Question 2.

Construct a parallelogram PQRS in which PQ = 6 cm, ∠Q = 120° and ∠RPQ = 30°.

Solution:

Steps of construction :

(i) Draw a line segment PQ = 6 cm.

(ii) At P, draw a ray making an angle of 30° and at Q

a ray making an angle of 120° intersecting each other at R.

(iii) With centre P and radius QR and with centre R

and radius equal to PQ, draw arcs intersecting each other at S.

(iv) Join SP and SR.

PQRS is a required parallelogram.

Question 3.

Construct a rectangle ABCD in which diagonal AC = 7 cm and the diagonals BD and AC intersect at O such that ∠BOC = 45°.

Solution:

Steps of construction :

(i) Draw AO= \(\frac{1}{2}\)AC = (\(\frac{1}{2}\) × 7) cm = 3·5 cm and produce AO to C

such that OC = OA = 3·5 cm.

(ii) At O, construct ∠COP = 45°.

(iii) From OP, cut off OD = \(\frac{1}{2}\) AC = 3·5 cm.

produce DO to B such that OB = OD = 3·5 cm.

(iv) Join AB, BC, CD, DA. Then ABCD is the required rectangle.