Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are $\frac{3}{4}$ time the corresponding sides of ΔABC.

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Solution

We have to draw a triangle

Then we have to construct a similar triangle with side of

Steps of construction

1. Draw a line segment

2. At B draw so that a ray BX is made

3. Keep compass at B and mark an arc of 5 cm at ray BX and name that point as A

4. Join AC to make

5. Draw a ray making an acute angle with BC.

6. Mark 4 points, B₁, B₂, B₃, and B₄ along BY such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄.

7. Join CB₄

8. Through the point B₃, draw a line parallel to B₄C by making an angle equal to ∠BB₄C, intersecting BC at C′.

9. Through the point C′, draw a line parallel to AC, intersecting BA at A′.

Thus, ΔA′BC′ is the required triangle.

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Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 34 time the corresponding sides of ΔABC.

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are $\frac{3}{4}$ time the corresponding sides of ΔABC.