Chapter 8 Construction of Triangles Ex 8.1

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 8 Construction of Triangles Ex 8.1

Case I: To construct a triangle when all the three sides are given.

Question 1.
Construct a triangle ABC where AB = 4 cm, BC = 5 cm and CA = 6 cm.
Solution.
Steps of construction:

1. Draw BC = 5 cm.
2. With B as centre, draw an arc of radius 4cm
   
3. With C as can be, draw arc of radius 6 cm Which cuts the former arc at A.
4. Join AB and AC.
5. Hence, ∆ABC is the required triangle.

Question 2.
Two points A and B are at a distance of 6.5 cm. Find a point C at a distance of 7 cm from A and 6 cm from B.
Solution.
Steps of construction:

1. Draw base AB = 6.5 cm.
2. Take A and B as centre, draw arcs of radii 7 cm and 6 cm above the line and below the line which intersects at C and C’.
   
3. Join AC, BC and C’A and C’B.
4. Hence, ∆ABC and ∆ABC’ are the required triangles.

Question 3.
Construct a ∆ABC where a = 6.5 cm, b = 7.2 cm, c = 8 cm. Draw the bisector of ∠B which meets AC at the point M.
Solution.
Steps of construction:

1. Draw AC = 7.2 cm.
2. By taking A as centre, draw an arc of radius 8 cm.
3. Again take C as centre and draw an arc of radius 6.5 cm which cuts the previous arc at B.
   
4. Join AB and AC. This gives the required ∆ABC.
5. Now draw BM as bisector of ∠B which meets AC at M.

Question 4.
Construct a triangle ABC where a = l cm, b = 5 cm and c = 4 cm. Draw perpendicular from A on BC.
Solution.
Steps of construction:

1. Draw a = 7 cm.
2. With centre B, draw an arc of radius 4 cm.
   
3. With centre C, draw another arc of radius 5 cm which cuts the former arc at A.
4. With centre A, draw ⊥ on BC i.e. AP.
5. Join AB, AC and AP.
   Hence, ∆ABC is the required triangle.

Question 5.
Construct an equilateral triangle whose sides are of length 5.5 cm.
Solution.
Steps of construction:

1. Draw BC = 5.5 cm.
2. With B as centre, draw an arc of radius 5.5 cm.
   
3. With C as centre, draw another arc of radius 5.5 cm, which cuts the former arc at A.
4. Join AB and AC.
   Hence, ∆ABC is required equilateral triangle.

Question 6.
Construct an isosceles triangle whose base is of length 3 cm and the other sides are of 5 cm each.
Solution.
Steps of construction:

1. Draw base BC = 3 cm.
2. With centre B, draw an arc of radius 5 cm.
   
3. With centre C, draw another arc of radius 5 cm which cuts the former arc at A.
4. Join BA and CA.
   Hence, ∆ABC is the required isosceles triangle.