Chapter 8 Construction of Triangles Ex 8.5

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 8 Construction of Triangles Ex 8.5

Question 1.
Construct a ∆XYZ where ∠XYZ = 60°, XY = 5 cm and XZ = 4.5 cm. How many such triangles are possible?
Solution.
Steps of construction:

1. Draw a straight line YA.
   
2. With Y as centre, draw an ∠BYA = 60°.
3. Taking Y as centre, draw an arc of radius 5 cm which cuts the ray BY at X.
4. By taking X as centre, draw an arc of radius 4.5 cm which cuts the base line YA at Z.
5. Join XZ.

Hence, required triangle XYZ is obtained.
In this case, only one triangle is possible.

Question 2.
Construct a ∆PQR where ∠PQR = 45°, PQ = 6 cm and PR = 5 cm.
Solution.
Steps of construction:

1. Draw PQ = 6 cm as base line.
2. At Q, draw an angle of 45° with the help of ruler and compass.
   
3. With centre P, take an arc of radius 5 cm which cuts the angle line and mark it as R.

Question 3.
Construct ∆ABC where a = 5.4 cm, b = 6.8 cm and ∠A = 45°. Can two triangles be drawn in this case?
Solution.
Steps of construction:

1. Draw a straight line AX.
2. Draw an angle of 45° at A i. e., ∠XAY = 45°.
3. By taking A as centre, cut an arc of radius 6.8 cm which intersects AY at C.
4. Now with centre C, draw an arc of radius 5.4 cm which cuts the base line AX at B and B’.
   
5. Join B and B’ to C.
6. Hence ∆AB’C and ∆ABC are the required triangles.
   Yes, in this case we can draw triangles.