R s aggarwal solutions mathematics class 9 Solutions for Chapter 13 geometrical constructions

Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part.

Draw an angle of 80 with the help of a protractor and bisect it. Measure each part of the bisected angle.

Construct an angle of 90 using ruler and compasses and bisect it.

Construct each of the following angles, using ruler and compasses:

(i) 75

(ii) 37.5

(iii) 135

(iv) 105

(v) 22.5

Construct a △ ABC in which BC = 5cm, AB = 3.8cm and AC = 2.6cm. Bisect the largest angle of this triangle.

Construct a △ ABC in which BC = 4.8cm, ∠B = 45 and ∠C = 75. Measure ∠A.

Construct an equilateral triangle, each of whose sides measures 5cm.

Construct an equilateral triangle each of whose altitudes measures 5.4cm. Measure each of its sides.

Construct a right-angled triangle whose hypotenuse measures 5cm and the length of one of whose sides containing the right angle measures 4.5cm.

Construct a △ ABC in which BC = 4.5cm, ∠B = 45o and AB + AC = 8cm. Justify your construction.

Construct a △ ABC in which AB = 5.8cm, ∠B = 60 and BC + CA = 8.4cm. Justify your construction.

Construct a △ ABC in which BC = 6cm, ∠B = 30 and AB – AC = 3.5cm. Justify your construction.

Construct a △ ABC in which base AB = 5cm, ∠A = 30 and AC – BC = 2.5cm. Justify your construction.

Construct a △ PQR whose perimeter is 12cm and the lengths of whose sides are in the ratio 3: 2: 4.

Construct a triangle whose perimeter is 10.4cm and the base angles are 45 and 120.

Construct a △ ABC whose perimeter is 11.6cm and the base angles are 45 and 60.

In each of the following cases, given reasons to show that the construction of △ ABC is not possible:

(i) AB = 6cm, ∠A = 40 and (BC + AC) = 5.8cm

(ii) AB = 7cm, ∠A = 50 and (BC – AC) = 8cm

(iii) BC = 5cm, ∠B = 80, ∠C = 50 and ∠A = 60

(iv) AB = 4cm, BC = 3cm and AC = 7cm.

Construct an angle of 67.5 by using the ruler and compasses.

Construct a square of side 4cm.

Construct a right triangle whose one side is 3.5cm and the sum of the other side and the hypotenuse is 5.5cm.

Construct a △ ABC in which ∠B = 45, ∠C = 60 and the perpendicular from the vertex A to base BC is 4.5cm.