Question

Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Construct a triangle similar to ∆ABC with scale factor `5/7`. Justify the construction.

Answer 1

Steps of construction:

1. Draw a line segment AB = 5 cm.

2. From point B, draw ∠ABY = 60° on which take BC = 6 cm.

3. Join AC, ∆ABC is the required triangle.

4. From A, draw any ray AX downwards making an acute angle.

5. Mark 7 points B₁, B₂, B₃, B₄, B₅, B₆ and B₇ on AX, such that AB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅ = B₅B₆= B₆B₇.

6. Join B₇B and from B₅ draw B₅M ॥ B₇B intersecting AB at M.

7. From point M draw MN ॥ BC intersecting AC at N. Then, ∆AMN is the required triangle whose sides are equal to `5/7` of the corresponding sides of the ∆ABC.

Justification:

Here, B₅M ॥ B₇B  .....(By construction)

∴ `(AM)/(MB) = 5/2`

Now, `(AB)/(AM) = (AM + MB)/(AM)`

= `1 + (MB)/(AM) = 1 + 2/5 = 7/5`

Also, MN || BC

∴ ∆AMN ∼ ∆ABC

Therefore, `(AM)/(AB) = (AN)/(AC) = (NM)/(BC) = 5/7`