Draw a ∆ABC in which AB=5 cm, BC=6 cm, and ∠ABC=60°. Construct a triangle similar to ABC with scale factor Justify the construction.

Steps of construction

1. Draw a line AB=5 cm.

2. Draw ∠ABY=60° on which take a length BC=6 cm.

3. Join AC.

4. Draw any ray AX downwards making an acute angle.

5. Mark 7 points B_{1},B_{2},B_{3},B_{4},B_{5},B_{6} and B_{7} on AX_{1} such that AB_{1}=B_{1}B_{2}=B_{2}B_{3}=

B_{3}B_{4}=B_{4}B_{5}=B_{5}B_{6}=B_{6}B_{7}

6. Join B_{7}B and from B_{5} draw B_{5}M||B_{7}B intersecting AB at M.

7. Draw MN││BC intersecting AC at N Then, ∆AMN is the required triangle whose sides are equal to of the corresponding sides of ∆ABC.

By construction,

B_{5}M││B_{7}B

∴ AM/MB = 5/2

Now,

⇒

Also,

MN||BC

∴ Δ AMN ~ ΔABC

∴

5