Draw a triangle ABC with side BC = 7 cm, ∠ B = 45°, ∠ A = 105°. Then, construct a triangle whose sides are times the corresponding sides of ∆ABC.

Question

Philoid · Accepted Answer

Steps of construction:

1. Draw a line segment BC = 7 cm.

2. Draw ∠ABC = 45° and ∠ACB = 30° i.e. ∠BAC = 105°.

We obtain ΔABC.

3. Draw a ray BX making an acute angle with BC. Mark four points B₁, B₂, B₃,B₄ at equal distances.

4. Through B₃ draw B₃C and through B₄ draw B₄C₁ parallel to B₃C.

Then draw A₁C₁ parallel to AC.

∴ A₁BC₁ is the required triangle.