Question

Construct a △ABC in which B = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°

Answer 1

Steps of Construction:

Step 1: Draw a line segment BC = 6.5 cm.

Step 2: With B as center, draw an angle of 60°.

Step 3: With B as center and radius equal to 4.5 cm, draw an arc, cutting the angle at A

Step 4: Join AB and AC.

Thus, △ABC is obtained.

Step 5: Below BC, draw an acute ∠CBX.

Step 6: Along BX, mark off four points B₁,B₂,B₃,B₄. such that

BB₁ = B₁B₂ = B₂B₃ = B₃B₄.

Step 7: Join B4C.

Step 8: From B₃. draw B₃D || B₄C, meeting BC at D.

Step 9: From D, draw DE || CA, meeting AB at E.

Thus, △EBD is the required triangle, each of whose sides is \(\frac{3}{4}\) the corresponding sides of △ABC.