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.

Question

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.

Philoid · Accepted Answer

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 B₁,B₂,B₃,B₄,B₅,B₆ and B₇ on AX₁ such that AB₁=B₁B₂=B₂B₃=

B₃B₄=B₄B₅=B₅B₆=B₆B₇

6. Join B₇B and from B₅ draw B₅M||B₇B 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,

B₅M││B₇B

∴ AM/MB = 5/2

Now,

⇒

Also,

MN||BC

∴ Δ AMN ~ ΔABC

∴