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 Δ ABC.

Question

Draw a triangle ABC with side BC = 7 cm, &#x2220; B = 45&#xB0;, &#x2220; A = 105&#xB0;. Then, construct a triangle whose sides are times the corresponding sides of &#x394; ABC.

Philoid · Accepted Answer

Steps of construction:

i. Now in order to make a triangle, draw a line segment BC = 7 cm.

ii. Now, construct an angle of 45^o at point B and 30^o at point C (because 45 + 30 + 105 = 180).

iii. Then, join the lines from points B and C to point A.

This gives us the required triangle ABC.

iv. Dividing the Base, construct a ray BX forming an acute angle from point B.

v. Plot 4 points on BX such that:

BB₁ = B₁B₂ = B₂B₃ = B₃B₄.

vi. Join B₃ to C.

vii. Now, draw a line from B₄ parallel to B₃C such that it meets line BC at C’.

viii. Draw A’C’ || AC.

Triangle A’BC’ is the required triangle.