Question

Construct a triangle ABC with side BC = 6 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are `(3)/(4)` times the corresponding sides of the ΔABC.

Answer 1

Steps of construction

(1) Draw BC = 6 cm.

(2) At point B, draw ∠XBC = 45°

(3) Using Angle Sum Property in ∆ABC, 
∠A + ∠B + ∠C = 180°
105° + 45° + ∠C = 180°
∠C = 30°
And, now draw ∠YCB = 30°

(4) Now, line YC and XB intersect at point A. Thus this is our required triangle ABC.

(5) Draw an acute angle ∠CBZ at B.

(6) Now cut 4 equal arcs BB₁, B₁B₂, B₂B_3, and B₃B₄ on BZ.

(7) Now, join B₄ to C.

(8) Draw a line parallel to B₄C from B₃ which intersects BC at C'.

(9) Now, draw a line parallel to AC from C' which intersects BX at A'.

(10) Thus, ∆ABC is our required triangle whose sides are `(3)/(4)` times the corresponding sides of ΔABC.