Question

Construct a ΔABC with BC = 6 cm, ∠B = 60° and AB = 5 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ΔАВС.

Answer 1

Steps of construction:

Step 1: Construct the original triangle ABC

1. Draw a horizontal line segment BC of length 6 cm.

2. Place your compass at point B and construct an angle of 60°. Draw a long ray BX along this angle.

3. Set your compass width to 5 cm. Place the compass needle at point B and draw an arc that intersects the ray BX. Mark this intersection point as A.

4. Join point A to point C using a straightedge to complete triangle ABC.

Step 2: Construct the similar triangle

5. Draw a ray BY starting from point B, pointing downwards to make an acute angle with the line segment BC.
6. Use a compass with a fixed width to mark 4 equidistant points on ray BY. Label these points B₁, B₂, B₃ and B₄ so that BB₁ = B₁B₂ = B₁B₂ = B₂B₃ = B₄B₄.

7. Join the fourth point B4 to point C with a straight line.

8. Go to the third point B₃. Draw a line from B₃ that is parallel to the line B₄C. Mark the point where this line crosses segment BC as C'.

9. From point C', draw a line parallel to the side CA. Mark the point where this line crosses segment AB as A'.

Triangle A'BC' is the required triangle whose sides are `3/4` times the corresponding sides of triangle ABC.