Question

Construct a triangle with sides 4 cm, 5 cm and 6 cm. Then construct another triangle whose sides are `2/3` times the corresponding sides of the first triangle.

Answer 1

Steps of construction:

1. Draw a line segment BC = 5 cm.
2. With B as centre and radius, AB = 4 cm, draw an arc.
3. With C as centre and radius, AC = 6 cm, draw another arc, intersecting the arc drawn in step 2 at the point A.
4. Join AB and AC to obtain ΔABC.
5. Below BC, make an acute angle ∠CBX.
6. Along BX mark off three points B₁, B₂, B₃ such that BB₁ = B₁B₂ = B₂B₃.
7. Join B₃C.
8. From B₂, draw B₂C" || B₃C.
9. From C", draw C"A' || CA, meeting BA at the point A'.
   Then A'BC' is the required triangle.