Question

Draw a triangle ABC with side BC = 6 cm, ∠C = 30° and ∠A = 105°. Then construct another triangle whose sides are `2/3` times the corresponding sides of ΔABC.

 

Answer 1

Given:

BC = 6 cm, ∠C = 30° and ∠A = 105°

∴∠B = 180° − (∠A + ∠C) (In ΔABC, ∠A + ∠B + ∠C = 180°)

= 180° − (105° + 30°)

= 45°

Steps of construction:

1. Draw a line BC = 6 cm.

2. Draw a ray CN making an angle of 30° at C.

3. Draw a ray BM making an angle of 45° at B.

4. Locate the point of intersection of rays CN and BM and name it as A.

5. ABC is the triangle whose similar triangle is to be drawn.

6. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

7. Locate 3 (Greater of 2 and 3 in`2/3`) points B₁, B₂ and B₃ on BX so that BB₁ = B₁B₂ = B2B₃ .

8. Join B₃C and draw a line through B₂ (Smaller of 2 and 3 in `2/3`) parallel to B₃C to intersect BC at C’.

9. Draw a line through C’parallel to the line CA to intersect BA at A’.

10. A’BC’ is the required similar triangle whose sides are `2/3` times the corresponding sides of ΔABC.