Question

Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.

Answer 1

Steps for construction:
1. Draw a line segment AB = 5 cm.
2. At B construct m∠ABC = 60°
3. Take a measure of 6 cm, and draw an arc from B on BC.
4. Join AC to obtain ΔABC.
5. Below AB, make an acute angle ∠BAX.

6. Since 7 > 5, mark off 7 points A₁, A₂, A₃, A₄, A₅, A₆ and A₇ such that  AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆ = A₆A₇.
7. Join A₇B.
8. Since we have to construct a triangle each of whose sides is 5/7 of the corresponding sides of ABC. So take five parts out of seven equal parts on AX. i.e. from point A5,      draw A5B' || A7B, meeting AB at B'.
9. From B', draw B'C' || BC, meeting AC at C' 
10.ΔAB'C' is the required, each of the sides is five-seventh of the corresponding sides of ΔABC.