Chapter 8 Construction of Triangles Ex 8.4

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 8 Construction of Triangles Ex 8.4

Question 1.
Construct a right-angled triangle the length of whose hypotenuse is 5 cm and one of the remaining side is 3 cm long.
Solution.
Steps of construction:

1. Draw a line segment AB = 3 cm.
2. Take A as a centre, draw an angle of 90° by ruler and compass.
3. Join angle line.
   
4. Take B as centre, draw an arc of radius 5 cm which cuts the angle line at the point C. Join BC.
   Hence, ∆ABC is required right-angled triangle.

Question 2.
Construct a triangle ABC when ∠A = 90°, AC = 5.4 cm and hypotenuse BC = 10 cm.
Solution.
Steps of construction:

1. Draw a line segment AC = 5.4 cm.
   
2. Take A as centre, draw an angle of 90° by ruler and compass.
3. Take C as centre and draw an arc of radius 10 cm which intersects the angle line at B.
4. Join B to C.
   Hence, ∆ABC is the required right angled triangle.

Question 3.
Construct a right angled triangle ABC whose ∠A = 90° and a = 10 cm and c = 6 cm, from the vertex A, draw a perpendicular on the hypotenuse.
Solution.
Steps of construction:

1. Draw a line segment AB = 6 cm as base.
   
2. With A as centre, draw an angle of 90°.
3. With B as centre, draw an arc of radius 10 cm which intersects the angle line at C.
4. Again A as centre, draw perpendicular bisector of BC.
   Hence, ∆ABC is the required right angled triangle.