Question

Construct a triangle of scale AB = 2.3 cm, BC = 4 cm and AC = 2.9 cm and then construct a triangle similar to a given ΔABC whose sides are 2/3 of the corresponding sides of the triangle. Also, write the steps of construction.

Answer 1

Let the triangle with sides 2.3 cm, 4 cm and 2.9 cm be ΔABC

Step1: construct segment AC of 2.9 cm

Step2: take distance 2.3 cm in compass keep the needle of the compass on point A and mark an arc above AC

Step3: take distance 4 cm in compass keep the needle of the compass on point C and mark an arc intersecting the arc drawn in step2. Mark intersection point as B join AB and AC

Step5: take any distance in compass and keeping the needle of the compass on point A cut an arc on ray constructed in step4 and name that point X₁. Keeping the distance in compass same keep the needle of the compass on point X₁ and cut an arc on the same ray and mark that point as X₂. Draw 3 such parts (greater of 2 and 3 in 2/3), i.e. by repeating this process mark points upto X₃

Step6: join X₃ and C and from X₂ (because X₂ is the second point 2 being smaller in 2/3) construct line parallel to X₃C and mark the intersection point with AC as D

Step7: construct line parallel to BC from point D and mark the intersection point with AB as E thus ΔADE ~ ΔACB is ready