Question
Construct a ΔABC in which BC = 6 cm, m∠BAC = 60° and median through A is 4.5 cm. Construct a ΔA ‘BC’ similar to ΔABC with BC’ = 8 cm.
Solution
Steps of Construction:
(i) Draw a line segment BC = 6 cm.
(ii) Draw a ray BX making an angle 60° with BC.
(iii) Through B, draw MB ⊥ BX.
(iv) Draw perpendicular bisector of BC which intersects BC at D and MB at O.
(v) With O as centre and OB as radius draw a circle.
(vi) With D as centre and 4.5 cm as radius, draw an arc which intersects the circle at A.
(vii) Join AB and AC. ΔABC is the required triangle.
(viii) Produce BC to C’, such that BC’ = 8 cm.
(ix) Through C’, draw C’A || CA which meets BA produced at A’.
Thus A’ BC’ is the required triangle similar to triangle ABC.
