Question

Construct a ΔABC in which BC = 8 cm, ∠B = 45° and ∠C = 60°. Construct another triangle similar to ΔABC such that its sides are `3/5` of the corresponding sides of ΔABC.

Answer 1

Steps of Construction:
Step 1: Draw a line segment BC = 8cm.
Step 2: At B, draw ∠XBC = 45°.

Step 3: At C, draw ∠YCB = 60°.Suppose BX and CY intersect at A.
Thus, ΔABC is the required triangle
Step 4: Below BC, draw an acute angle ∠ZBC.
`"Step 5: Along BZ, mark five points "Z_1,Z_2,Z_3,Z_4 and Z_5  "such that"  BZ_1 = Z_1 Z_2 = Z_2 Z_3 = Z_3 Z_4 = Z_4 Z_5`
Step 6: Join CZ₅ .
Step 7: From Z₃, draw  Z₃ C ' ||CZ₅ meeting BC at C’.
Step 8: From C’, draw A'C' || ACmeeting AB in A’.

Here, ΔA'BC ' is the required triangle whose sides are `3/5`of the corresponding sides of ΔABC.