Chapter 8 Construction of Triangles Ex 8.3

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 8 Construction of Triangles Ex 8.3

Case III: To construct a triangle when a side and two angles are given.

Question 1.
Construct a triangle PQR when QR = 8 cm, ∠Q = 120° and ∠R = 30°
Solution.
Steps of construction:

1. Draw line segment QR = 8 cm.
   
2. With Q as centre, draw an angle of 120°.
3. Again with centre, draw an angle of 30° which intersects the arms of angle 120° at P.
   Hence, ∆PQR is the required triangle.

Question 2.
Construct a triangle ABC when b = 7 cm, ∠A = 90° and ∠C = 60°.
Solution.
Steps of construction:

1. Draw line segment b = 7 cm as base.
   
2. Take A as centre, draw an angle of 90° by ruler and compass.
3. Take C as centre and draw an angle of 60° by ruler and compass which will meet the angle line at B.
4. Join B to C.
   Hence, ∆ABC is the right-angled triangle.

Question 3.
Construct an isosceles triangle whose base is of length 4 cm and the vertex angle is equal to 30°. Draw a perpendicular from the vertex to the base.
Solution.
∵ Vertex angle = 30°

Steps of construction:

1. Draw a line segment BC = 4 cm as base.
2. With B as centre, draw an angle of 75°.
3. With C as centre, also draw an angle of 75° which intersects at A.
4. Draw a perpendicular from the vertex A to the base BC.

Hence, ∆ABC is the required isosceles triangle whose base is 4 cm and vertex angle = 30°.